nm0658: this is the last of five sessions which are specially for your group to 
look at the design analysis of experiments er from next week we are going back 
to the general group and we're going to look at advanced methods which i think 
are equally applicable for everybody so we're then going to look at advanced 
modelling ideas which i think are the same sort of models you need to consider 
whether you're doing a survey or an experiment the two main problems we will 
tackle there will be what happens if your design is unbalanced and some 
experiments are unbalanced and most surveys have unbalanced data and the second 
thing we will tackle is what happens when your data may not come from a normal 
distribution the traditional statistics says that if your data come from a 
normal distribution then everything is fine and if they don't come from a 
normal distribution then you first panic and then you transform your data and 
then you hope your panic is over and there are 
modern methods now where you can analyse data from a non-normal distribution 
much more flexibly than was possible before so that's what we're going to do 
together with the er students from wildlife management er and also from 
vegetation surveys so what i want to do today is to review the ideas er of 
experimental design and analysis and then go through one more advanced topic 
which is a very common topic and which is the subject of repeated measures so 
that's where you measure repeatedly on the same unit be it the same animal the 
same tree or the same plot you go back to it perhaps repeatedly through the 
season and what i want you to do with this single example of a more advanced 
method is to see whether the weapons you have learned through the last four 
weeks how much can they help because what i would like you to get to by the end 
of this course is er so that the subject of statistics is not always expanding 
you've got to give yourself a framework so that when 
you have a new problem you say well what parts of the problem are new and what 
parts can fit into the the subject that i already know and i want to show you 
that although repeated measures appears to be a new subject once you understand 
some of the basic ideas we've tried to cover then there are only a few extra 
changes to be able to follow the ways you could analyse a repeated measures 
example so what i'm going to do this morning is to review some of the ideas of 
designing experiments bringing in what Genstat can do to help you look very 
quickly at data management er and then go into as part of the analysis how to 
analyse a repeated measures experiment [cough] you should have just two 
handouts although it says here you have three i couldn't think of anything 
extra to write for the worksheet so this is the one week where there isn't a 
worksheet so you have a lecture note and you have the practical exercise for 
the practical er which is as usual in the Met department at 
eleven o'clock [cough] now we're going to look at the ideas of designing 
experiment and i've kept repeating that you start with your objectives they 
lead to the treatments the way you're doing your experiment leads to the layout 
you must decide on your measurements and we've now moved for the last four 
weeks to do the analysis and we're going to consider these components in turn 
yet again and see at the same time how Genstat can assist with the 
randomization of an experiment so the menu that you're going to use here we see 
Genstat it's not very clear but it's probably clearer on your slide er that 
you're on the usual stats menu but instead of going to analysis of variance you 
go up one to an option called design and there are a variety of things you can 
do and all we're going to do is look at one or two standard designs and we're 
going to use them first to show you how to randomize an experiment but also to 
review some of the ideas of different experiments here's the 
sort of menu you get and almost all the experiments that we've been discussing 
you can randomize using this menu for the very simplest experiment you might 
consider is a one-way design where you've just got treatments and the 
experiment is laid out in randomized blocks so then in this menu you have to 
say what do i call the blocks we've just left it with an A block and how many 
blocks are there what are we going to call the units well we'll call them plots 
and what are we going to call the treatment factor which might be variety here 
i've just called it treat and how many levels 
sm0659: one question please what is the criteria for one-way or two-way two-
ways design 
nm0658: you mean this 
sm0659: yeah what will be the criteria for this to choose one-way or 
nm0658: two-way designs 
sm0659: yeah i believe there must be a two-way 
nm0658: this is where on the second component i've said that you first think of 
the treatments if you're if you have one treatment factor like variety that is 
a one-way design if you have two treatment factors let us say three varieties 
and two levels of fertility that would be two treatment factors and then you 
would have a two-way 
design in randomized blocks 
sm0659: different ways for the 
nm0658: well when you have 
sm0659: bias in the experiment 
nm0658: when you have a one-way design it's simple whether you call it a factor 
or a treatment it's just the same thing when you have a two-way design take the 
example i've given you where you have three varieties and two levels of 
fertility you can either think of this as a two-way design for the treatments 
or you can think of it as a one-way design where that one way has six 
treatments because it's you can think of it as three by two or you can think of 
it as the six and it's up to you whether you want to think of it as just six 
treatments or whether you want to say well i would like to know right from the 
beginning the layout of my experiment in terms of both factors so when it's 
more complicated than a one-way design you can choose whether to take all 
combinations of the treatment factors and call them one big factor with all 
those levels or to split it up by the components [cough] 
sf0660: do you ever have three-way design 
nm0658: ooh 
lots of times 
sf0660: so it's like er on the er er dialogues within 
nm0658: yes 
sf0660: and you just have one and two-way and then generalize the model 
nm0658: this is this parallels here what you would have for the analysis 
sf0660: yeah 
nm0658: and you can either choose to do the analysis thinking what is my design 
let me give it a name or and i prefer to say it's a general design 
sf0660: mm 
nm0658: how many treatment factors do i have and this menu system because it's 
for simple designs only it only allows you up to five factors but five is 
probably enough so if you go to the general then it would say how many 
treatment factors do you have and you could have up to five different treatment 
factors there's no limit in Genstat on the number of treatment factors but we 
find most experiments five is enough i would like one of the main bits of work 
i did when i was working in er in Niger was to try and encourage people who 
only had experiments with one or two factors er to include more factors once 
you click on okay this is what you will get so you will now get a Genstat 
spreadsheet and you can see here er let me return to 
this previous slide just to remind you what i did this particular example i 
have four blocks and three levels of the treatment so it's a simple design i 
have twelve plots so there's a twelve down at the bottom which Genstat works 
out automatically just multiplying the four by the three that this was an 
experiment with twelve plots so when i click on okay it will produce the 
randomization and automatically you will now get i've called it data but it's 
really just the design you will now get this structure in a Genstat spreadsheet 
now i want you to notice and we will emphasize this later on that this way of 
laying out the data is part of the simple data management and i've seen one or 
two examples this term because you are all addicts of Excel you will find that 
Excel gives you too much freedom in laying out your data and that can cause 
lots of problems later on so i emphasize what we discussed in session three 
that when you have twelve plots in an experiment the 
layout of the data for a statistics package is to have twelve rows of data one 
for each plot you will have the label for the plot and you will then have 
another column which says which block am i using which plot do i have and which 
treatment and these treatments have been randomized so there's your 
randomization so this is your data laid out in the sort of field order ready to 
add further columns if you like with your measurements once you take them and 
so this is all ready to be a data collection form and this is in Genstat so the 
next part of your strategy you see is to say well after i haven't got any 
measurements yet because i'm just designing my experiment but when i've got my 
measurements they will make more columns here do i want to enter these 
measurement data into Genstat or into Excel i can choose so if you choose to 
save this as an Excel file which i did then here is the same information saved 
in Excel so now as you see you've got A B C and D in Excel and 
once you measure a few things the height of the plants or the mean height of 
the plants er the yield and various things those just become more columns which 
you can enter into back into Genstat for the analysis and you will remember 
from the er session on management we have said please enter your data straight 
from the field in the randomized order and now you see that's a very easy 
routine you can start in your stats package to randomize your experiment if you 
choose to do your data entry in Excel then that's fine you export all the 
details before the season here you now collect data and as you collect the data 
you just type in your extra columns of data and your data are ready entered 
and in many of the courses that i give i try and encourage scientists not to 
enter data at the end of the season when they've got everything collected but 
if after a few weeks you've measured the data fifty per cent flowering then the 
day you measure it you just type it in it's very quick and so it's there in 
your field book and in it goes same day and then if there's a problem you can 
probably have a look very quickly and you've seen how easy it is to having even 
if you enter in Excel to then get your data into Genstat for the analysis so 
the very day you collect your data there is no problem doing your first 
analysis and the procedure works very nicely any questions so far [cough] the 
second example this now can follow up your initial question this is now an 
experiment where i have got three factors so i've got three treatment factors 
i'm assuming irrigation with four 
levels i'm assuming fertility with two levels i'm assuming variety with three 
levels so i'm assuming a much more complicated experiment er how many 
treatments 
sm0661: twenty-four 
nm0658: twenty-four treatments so we're just taking we're going to have an 
experiment with all levels of these this would be a simple experiment which 
would mean the total number of treatments is twenty-four so i could enter this 
as a one-way design with a treatment factor going from one to twenty-four and 
associate each number with a combination of irrigation fertility or variety or 
i could choose to enter straight away and say i want to do this and er 
randomize it straight away for my irrigation fertility and variety i've decided 
to have four replicates and i assume also i've decided to have a split plot 
design and in my split plot design i'm going to have my level of irrigation and 
fertility on the main plots and i'm going to have my variety on the subplots i 
assume i've decided this maybe you decide this in 
conjunction with a statistician before you come to the experiment now you 
decide that's the design i would like to try [cough] so how many subplots in 
this experiment 
sm0662: 
nm0658: how many how many plots altogether you've already said there are twenty-
four treatments 
sm0663: ninety-six 
nm0658: there are ninety-six plots just twenty-four by four because i've got 
four replicates and how many main plots 
sm0664: eighteen 
sm0665: thirty-two 
sm0666: sixteen 
nm0658: sixteen let's have a look well the corresponding design dialogue this 
is an answer to your question now can you have more than two i now go to the 
general design i've chosen to make it split plot so i'm going to the general 
split plot design and it will now say to me how many treatment factors do you 
have so i must understand these questions what do i mean by a treatment factor 
which i hope you understand quite clearly from the course and how many of those 
treatment factors are on the subplots well my design that i was considering had 
two treatment factors on the main plot and one on the subplots how many 
replicates 
four on my main i'm going to call the main plot factor M plot i'm going to call 
the subplot factor subplot whole plot treatment factor one i'm going to say is 
irrigate whole plot treatment factor two i'm going to say is fertility with 
those number of levels and subplot treatment factor one variety has three 
levels 
sm0659: why is that 
nm0658: sorry 
sm0659: why is that 
nm0658: i chose that i decided that was my experiment you can have any number 
so you have to decide how many varieties do you have to compare 
sm0659: er why did you call those subplots variety 
nm0658: because i thought that that would be a factor which i didn't need big 
plots for that's part of the design process you have to you have to decide do 
you need the same size plots for all your factors if you don't then are there 
any factors that need larger plots than the others here irrigation obviously 
often needs large plots sometimes fertility levels need large plots because you 
get leaching from one plot to another and often varieties you can have quite 
small plots breeders have 
very small plots so i'm assuming that either because of your expertise or in 
discussion with a statistician you decide that you can get away with small 
plots for variety but you need larger plots for here and that's why you chose a 
split plot design if that had not been the case then as we've said before i 
would recommend that you don't have a split plot design you've have a 
randomized plot design and then you you'd just have a different menu and you 
just say these are the three factors and what i want to show you in a minute is 
that we'll come and check well was it a good idea our design 
sf0660: can i just ask what's the randomization seed is that the way of 
generating random numbers 
nm0658: that's correct er yes i haven't explained these things down at the 
bottom the randomization seed means that that's the point at which it starts 
its random number generation so if you were to make a note of this then you 
could always regenerate the same randomization yet again you don't have to keep 
everything by typing this number in yourself so usually you allow the 
computer to choose this and it's different every time but if you chose to make 
it the same you'd get the same randomization and that's quite a good way of 
keeping a record of the randomization you had without noting everything down if 
somebody would say please could you print me another copy of that well you can 
always print the resulting spreadsheet but if you said well sending the 
information all you have to do is fill this in this way and give that random 
number seed and you'll get the same randomization and this is the randomization 
that follows so this is the output when you press okay it goes on of course 
down to ninety-six plots we only have fourteen plots here but you see it gives 
you a column which says which block which main plot which subplot which level 
of irrigation which level of fertility and which variety these of course are 
not randomized but the this which is the level of irrigation fertility and 
variety that is associated is randomized to a 
certain extent what you should notice is that the variety is randomized on the 
little plots so here's the first main plot which goes one one one while the 
subplots go one two three you will notice that irrigate is at the same level 
one for all those three because that's at the main plot level and so is 
fertility but the varieties go one two three because they are randomized on the 
subplot level and when we go to the next main plot here we have main plot two 
subplots one two three these two again remain the same because it's a split 
plot design and these three this is a complete repeat of all the values here so 
each main plot is a total repeat for all the levels of variety but it just is 
one plot from here 
sm0667: er if they're completely randomized will it be numbers one to ninety-
six or 
nm0658: er sorry 
sm0667: if they're completely randomized 
nm0658: if it were completely randomized 
sm0667: mm 
nm0658: without even any replicates then it would randomize everything for the 
numbers one to ninety-six so you can choose do i have replicates which is a 
sort of blocking idea er do i have 
treatments and how do i randomize you probably wouldn't use this menu if you 
just wanted a set of random numbers there's an easier way of doing that but 
that would be the extreme for the randomization that's right now you asked just 
now about this randomization seed but there are other options down at the 
bottom that you could also ask for and i've used one or two of these er i've 
asked could i have a dummy ANOVA table which might answer a bit more of your 
question why did i choose to put varieties at the subplot level what i would 
like to see occasionally is is the resulting design a sensible one for me to 
continue with and so i could learn a little bit about that with a dummy ANOVA 
table and i will show you in a minute what that is i could ask for trial ANOVA 
with random data what it does there please don't make too much of that the 
random data is only there to show you what will the results look like from this 
sort of experiment when you have 
some data how will the results be laid out so it can show you the way in which 
the results will be laid out and i think that's quite useful ahead of the 
experiment to say is that a sensible thing so this is the sort of tool that i 
would like also for discussion with people such as yourself when you're saying 
i'm thinking of doing this sort of experiment and i can say well this is the 
sort of result you will get are you happy A with the design and B that you can 
then understand the results so let's show you what this works out because i 
ticked the dummy ANOVA table here i have the dummy ANOVA from Genstat i asked 
you how many main plots and you see this is straight print out from Genstat and 
here you see here is the main plot section so this is all revision but you can 
see that from the point of view of these two factors this is a simple 
experiment not with ninety-six plots but with ninety-six divided by three plots 
so there are thirty-two plots thirty-two main plots 
which is my twenty-one plus three plus one plus three plus the three plus the 
extra one so here we are at the main plot section so when you want to evaluate 
if this was a good experiment from the point of view of the main plots you can 
start having a look just up here was it a good experiment to study irrigation 
and fertility and the interaction 
and then when you come along to the subplot section you come along here and you 
have all the degrees of freedom down here ninety-five is the total because 
that's ninety-six minus one there's your n-minus-one [cough] i haven't given 
this but you'll try this in the practical Genstat also provides a sample ANOVA 
with random data to show you how the results will look and i find that quite 
useful in teaching and we're asking you to get this in the in the practical to 
have a look at that and the sort of question you can now answer is how would 
the degrees of freedom change if you moved fertilizer to the subplots if 
instead of having two main plot factors and one subplot factor you said well 
fertilizer could go on the little plots i wonder w-, how that would look and 
you have now two ways of doing that you can do that from first principles 
yourself or you could run the randomization again and move one of the factors 
from the main plot 
level to the subplot level i hope you can see from here if we move fertilizer 
from here down to here then this would come down here and also this would come 
down here so we would now be doing an experiment with three degrees of freedom 
there and just three values here because this stays and so this now the intera-,
the residual would have nine degrees of freedom we've got ourselves rather a 
small experiment at the main plot level that's not such a good idea so it's 
those sorts of things you can now do either by studying this or by running 
through the design again and that's what we've asked you to do in the practical 
any more comments or questions on this design part i'm now moving to data 
management 
sf0660: er i'd like to ask something on the number of plots that you have for 
your er main blocking practice the main treatment practice 
nm0658: yep 
sf0660: er from where he's given us the three factors 
nm0658: yes 
sf0660: er i don't know if you've got irrigation as four levels fertility two 
levels how do you then get can you not say that you had nine plots for your two 
nm0658: with the design as randomized that's what you've got 
sf0660: so for your main plot from that did you say you've got how many plots 
nm0658: for my main plot i said i've got thirty-two main plots which is the 
ninety-six that i had divided by three 
sf0660: but if you didn't go through that ANOVA table er is there any way of 
working that out just from what you get at the very beginning er structure 
nm0658: yes if i didn't have that at the beginning i would say that 
at the main plot level what i've got is four blocks 
sf0668: 
nm0658: and four levels of irrigation which is four times four 
sf0668: 
nm0658: times two levels of fertility which is four times four is sixteen times 
two is thirty-two 
sf0668: 
nm0658: any more questions the second topic 
sm0669: er excuse me er er did and the design in the in in reality 
nm0658: yeah 
sm0669: i was thinking how about three factors plot that's to say maybe to have 
the er irrigation out the way then the fertility as a subplot and then the 
variety as the sub-subplot in that case we will have been having more of a how 
will i call it degrees of freedom than irrigation and the fertility as a main 
plot and then having the variety as a subplot how would you 
nm0658: okay can anybody er let me repeat the question and then i'm interested 
if any of you can now provide an answer you are now you've had fifteen weeks of 
statistics so you're all semi-statisticians [laughter] now the question was 
that this was er deliberately something a little more complicated as an 
experiment than you've had before it had three factors and the question was 
well if you have three factors why did we just have a single split or if i 
understand your question correctly why didn't we have two splits where perhaps 
we have irrigation on the main plots and then we have er fertility on the sort 
of middle-size plots and variety on the little plots and that is quite common 
does anybody have any comments on that 
suggestion supposing that when you're back home and starting to work somebody 
says i'm doing a three factor experiment so i'm doing it on a split-split 
that's called a split-split plot design very difficult to say if you've had a 
few drinks [laughter] does anybody have any anybody have any comments on 
whether they would encourage that whether they would like that 
sm0670: 
nm0658: ah [laugh] 
sm0670: and it was how would we differentiate the effect of the two that you 
combine in that one like the the variety the irrigation in the block 
nm0658: yes here 
sm0670: combine make the main 
nm0658: i had here i had irrigation and fertility on the main plots 
sm0670: yes 
nm0658: yes 
sm0670: how would you s-, 
nm0658: how 
sm0670: how would you differentiate the effect on your experiment of 
nm0658: well if you look at the ANOVA table that's the same question as though 
you just did a randomized block design this is like a randomized block design 
and you'll have a set of treatment means which give you the mean for each level 
of irrigation and you will have another one which gives you the mean for each 
level of fertility just the two means 'cause there's only two levels and then 
you'll 
have another table for the interaction and that is one reason if you're not 
sure how that's going to look in practice that's one reason why Genstat gives 
you a dummy analysis not just with the degrees of freedom which you got here 
but also with random data so you can see how all the means will look and you 
can see i wonder if that will give me sufficient information to understand all 
the components of the treatments that i've applied to my experiment i think 
it's a similar question that most people feel that if they've got many factors 
they're much happier if each factor's at a different sort of level which leads 
you towards having two factors in a split plot experiment and three factors in 
a split-split plot and i hope you never have five factors because then you've 
got huge plots and and so on does does anybody have any thoughts about would 
you encourage 
sm0671: well just a general stab in the dark 
nm0658: yes have a s-, 
sm0671: you split your plot into levels of fertilizer and split it again and 
they're very small plots the smaller the sample er if you have a larger sample 
variations tend to be absorbed in a large sample rather than a small sample is 
that 
nm0658: that that's that's almost there 
sm0659: depends on the way degrees of freedom 
nm0658: degrees of freedom will come 
in er you would it would be like having the top level it would be like just 
having irrigation at the top level does anybody have any general feelings about 
whether they would encourage experiments to be at lots of different levels or 
whether they would re-, prefer information to be at a single level 
sm0672: 
sf0673: wouldn't it depend on what you're looking 
nm0658: i-, 
sf0673: at what you were interested in 'cause if you want to to find er equally 
the effect on irrigation and part of the effects of fertilizer and variety and 
on interactions then by splitting it up into several levels you're going to 
lose a lot of degrees of freedom for your upper levels 
nm0658: right 
sf0673: er so surely the information that you'll obtain will be er you won't 
have er i don't know how to finish that sentence 
nm0658: er let let me try and finish it for you well maybe try and ask somebody 
else 
sf0673: mm 
nm0658: because i think you were voting for the side of not having too many 
levels 
sf0673: mm 
nm0658: er there were other people who i think instinctively said let's have 
more levels is there anybody who would who approves of the idea of having lots 
of levels 
sm0671: in blocks why didn't we use one of those factors 
nm0658: right e-, each one going down 
sm0671: yeah that's the way they 
nm0658: right okay having your idea of having two factors in the split block 
design and three factors therefore in a split-split block design is extremely 
common my view is your other intervention which is to say let's not have too 
many levels unless we need to so the general view i have is that 
lots of levels causes complication if you can have your experiment at a single 
level life is simpler all your tables are compared at the same level all your 
plots are the same size and the analysis the design is simpler and i think the 
analysis is simpler so the split plot analysis has lots of different levels and 
you will find when you look at the standard errors that that indicates that the 
analysis becomes very messy and complicated so i would prefer not to have split 
plot experiments the only reason i would have a split plot experiment is if 
some factors need large size plots like irrigation and other factors don't and 
then if the l-, if irrigation needs large size plots and we want to have 
irrigation and variety if we want to have no different levels then all plots 
have to be very very large whereas because variety only needs small plots we 
can choose to split the large plots that we need for irrigation into 
subdivision that seems a good reason i find 
there is no other good reason for having split plot designs we will see later 
today that the whole nightmare of repeated measures analysis is a similar 
argument that the repeated measures are repeated within the plot they're like a 
sort of split plot where time is each measurement and you will find as soon as 
you have lots of different levels in your data your analysis is getting messier 
so i'm not very comfortable with the idea that if you increase the number of 
factors you also increase the layout problems remember at the very beginning 
we've said that when you look at design please think of your treatment 
structure we said we want three factors because that ties in with our 
objectives and then please think of your layout now what the people who do 
split-split plot all the time are doing is they are thinking of these two 
together 
the treatments and the layout and they keep confusing them together and i would 
like people to think of the treatments first and say i could satisfy my 
objectives by having three factors and there'd be lots of objectives i could 
satisfy now can i have a very simple layout a simple layout is a randomized 
complete block sort of layout with twenty-four plots in this case for each 
block and so there are no different levels for the treatments and if you can 
manage that please do it if you can't manage that you say well maybe i'll have 
to go to a split plot sort of layout with two levels but don't volunteer for it 
and say because i've got two factors i will automatically go for two levels i 
think that causes many problems in the analysis of experiments and is part of 
the reason people 
don't exploit their data as much as they could 
sm0669: er my last question er would you be able to tell what a reasonable 
portion is statistically speaking of the effects of say irrigation confidently 
then confidently them i was thinking when you split them and you could do these 
things see i would have gone in for irrigation as the main and then the er er 
fertility i mean the maybe the fertility that and then gradually move on to the 
variety and have an idea whether even there is an interaction between variety i 
mean irrigation 
nm0658: if you lay it out in a randomized block with just one level you can 
answer all those questions you can askn-, answer the questions about irrigation 
about variety and about the interaction whether it's laid out as a split plot 
or whether it's laid out as a randomized block so the questions you can answer 
about the treatments are the same there are some people who would argue that 
when it's laid out as a split plot compared to random and let me come back a 
step when it is laid out as a randomized block you are sort of treating each 
factor equally they are all on plots of the same size one of the arguments 
given in the textbooks for having a split plot is where you want more 
information in this case let's say on variety so you're going to put them on 
the little plots and then they're always close together and you ye-, you want 
less information on the irrigation so you put those on big plots that are by 
definition further apart on average and so when you compare a randomized block 
with a split plot in the split plot according to the textbooks you get more 
information on the subplot factors and less information on the main plot 
factors the problem i have is that you get much less on the main plot compared 
with a very little gain on the subplot and also that does not account for the 
fact you also add in unnecessary complication in interpreting the results which 
means that i don't like that as a reason for doing a split plot experiment the 
only reason i like is the fact that you have to for practical purposes and 
there are many of those okay the next subject then we'll have a break and we'll 
discuss repeated measures after the break now what i hope to show you is that 
the ideas of data management which we distributed in session three which was 
very early last term that was data management for any sort of data when we 
translate those ideas into experimental data 
experimental data are quite simple usually and so you shouldn't have any 
problem if you manage the data sensibly and if you keep the principles so we're 
going to review the standard ways of entering experimental data which i think 
follow automatically if you've understood the ideas of design and what we're 
also going to show you is what happens if your data have been entered 
differently and this is where we're hitting a new problem now because of all 
these people as i've said before who are maniacs for Excel and that means you 
can enter data in all sorts of crazy ways doesn't it er and and then you can 
have problems reorganizing your data so you can do the sensible analysis and i 
have to tell you that as statisticians now this is serious because in the olden 
days we found that we spent all our time helping people on the analysis now 
most of your time seems to be spent on rescuing your data from poor data 
management the analyses are very quick you just click on the 
ANOVA button in Genstat so the analysis step is very very quick and you've done 
it many times this term the step which isn't quick is reorganizing your data 
because they were entered in a funny way so there are two ways to avoid this 
and i want to indicate both of them the first is please enter your data 
sensibly and then you won't have this problem and the second is if you haven't 
entered your data sensibly please don't re-enter please use the computer to 
reorganize your data but accept that don't get annoyed at either Excel or at 
Genstat or Minitab because that's taking the time i'm afraid it is the data 
manipulation that does take the time so allow a little bit of time for that so 
we're going to show you both and you either need to reorganize the data because 
you've entered it in an odd way or because alternative analyses require 
different layouts so sometimes when the data aren't so simple you might have 
three different analyses and for one analysis it was good to 
enter the data across and for another analysis it was good to enter the data 
down so you need to become a little adept at data manipulation or you're going 
to waste a lot of time and a lot i do mean it perhaps i'll er tell you one er 
not horror story but close the subject of data management is not well reported 
in the textbooks when i arrived back a couple of years ago one of the first 
advisees i saw was somebody who was just finishing his PhD at Reading and he 
had been on this course but we hadn't been discussing much about data 
management in the olden days and he'd followed a little bit of the notes on how 
to organize the data and it was discussions with him that clarified to me that 
we must include data manipulation data management in this course which is why 
we've changed this course to include this he had an experiment which was done 
here and he'd done his experiment at two different places for each of the three 
years of his PhD and each experiment 
he had measured ten different things so he'd had ten measurements it's all very 
simple these were very simple experiments he had forty-eight plots in each 
experiment he had now looked in a textbook and he looked at his notes to see 
how to enter the data and he had entered the data quite nicely organized with 
three columns the first column was the yield or the measurement the second 
column was the block and the third column was the treatment there were twelve 
treatments and there were four blocks so he had measurement block treatment 
because he'd looked in a textbook and textbooks only seem to deal with 
experiments when you have a single measurement which is unlike the real world 
where you always have lots of measurements he decided to enter his ten 
measurements in ten different files so he now had ten little files each one 
with three columns the block and the treatment columns were the same and the 
measurement was different and then he had six experiments 
so he now had sixty files each one with three columns in and each one followed 
precisely the method of analysis he'd been taught in his course and he'd 
finished his analysis and he was three weeks away from submitting his PhD and 
his supervisor looked at his information and said there are two interesting 
things i would like you to do in addition the first is that i've noticed that 
you have measured the yield in two different ways i'd like you to do what's 
called an analysis of covariance where you adjust one measurement for the 
values of another measurement could you please do a bi-, a simple analysis of 
covariance for each of your six experiments and he gave him a very simple thing 
and showed him it was in the textbook the second question was even more 
perplexing to him he said could you do a simple combined analysis where you 
combine the information for the six experiments together to see how the results 
you have reinforce each other and so he came to 
statistics to do this he knew no computing he only knew how to turn the 
computing handle so he was now being asked a simple question of data management 
well it would have been simple if his data had been organized sensibly but can 
you see that this idea of covariance which would have been trivial with Genstat 
normally meant that he had two data files which he had to merge together 
because the two columns were in different files nobody'd taught him about 
merging files and the combining of the experiments the six experiment meant not 
just that you merged the files but you then had to put them end to end because 
he had forty-eight but now he wanted forty-eight times six with another column 
which said which experiment it was so when he came with three weeks to go we 
explained these ideas to him but because he had no concept of data management 
or of computer ideas such as merging files he never succeeded the only way it 
could possibly have happened is if somebody else had taken 
his data and done it all for him that's not his PhD or if he'd learned a little 
about data manipulation and these were very very simple tasks i have to say 
these are much easier tasks now you've got Windows than they were when you had 
to merge files using DOS commands 
but nevertheless this was not possible for him to do and that's data 
manipulation taken to its illogical extreme but i have to say that the way he 
was encouraged to enter the data first was exactly what was recommended in a 
very popular textbook which we use on our courses says when you're entering 
your data into the computer this is the sort of layout and it encouraged the 
layout which caused his disaster because it didn't say of course in practical 
experiments you will have more than one measurement and just put them end to 
end don't make them in a different file so let me just remind you this was the 
yield data that we discussed in session three you have nothing new you need to 
learn if you understood session three notice that the way that we have laid 
this out with the block numbers is exactly the same as the way Genstat has just 
randomized your experiment at the beginning so here are the blocks the 
repetitions and the treatments and here are the 
measurements that you just type in when you get them so as long as you don't 
mess things up from where you started the rules are very simple how many plots 
do you have each plot becomes a row each column is a measurement i can't think 
of anything that's more simple and that's what you have to do you will find 
that there's one complication which we do discuss in session three which is 
what happens if some of the measurements are made at the plant level or the 
plot level here sorry the plot level and other measurements are made at the 
plant level so for example it's very popular to measure the yield by harvesting 
at the plot level but you might measure the height of twenty plants in each 
plot i wonder how you would enter that to which the answer is either in Excel 
or in Genstat you have one sheet for your plot level and you have another sheet 
for your plant level and we've covered that both in the discussion in section 
three and in the practical that you did so as long 
as you're happy with those you don't have a data management problem you should 
enter your data in this way i can leap ahead a little bit to these repeated 
measures ideas supposing that here's an example i'm sorry it's a bit in French 
but this is the weight of small potatoes middling potatoes et cetera we're 
going later on to consider repeated measures which is measuring things after 
twenty days twenty-five days thirty days and things like that how should you 
enter those data answer they are just measurements so enter them across just as 
though you were entering different measurements so just because you made the 
measurements which differ in time don't get more complicated just treat them as 
a measurement and so if you have six repeated measurements just they're six 
measurements enter them across they haven't changed the number of plots in your 
experiment so they go across this is how not to enter experimental data this is 
the same data here we have the 
treatment information and here we've entered the data for replicate one 
replicate two replicate three for one measurement that is very popular isn't it 
[laugh] i i'm sorry i'm i'm looking at you because i-, i-, you know it's not 
you that's made this as a this is encouraged in many departments and it seems 
very obvious and it works quite well for simple problems also notice that if 
you were doing the analysis by hand in the olden days this is exactly what you 
would do because you could work out the mean of these and you could get the 
mean for that treatment so you could get all the treatment means down here and 
all the block means across here so if you are in the habit of confusing entry 
with analysis this is wonderful you can use Excel to work out calculated 
columns and it all seems to work quite well until you try and do a full 
analysis and then it all falls apart do not confuse analysis with entry if 
later on you want to analyse your data either with Genstat or Excel you can 
enter the data in the proper way that's like this if you would now like to look 
at the data like this i've said this is how not to enter experimental data if 
you want to look at the data like this that's terrific it's called tabulation 
you enter the data in long columns and then you say please tabulate the columns 
and across the top i want one factor and down here i want the other factor and 
then i'll put some summaries i don't have a problem looking at the data like 
that i have a problem entering the data it's confusing entry with analysis in 
Genstat that's called tabulation in Excel it's called pivot tables i don't care 
h-, whether you do it in Excel or whether you do it in Genstat so enter your 
data in Excel the proper way enter your data in Genstat the proper way if you 
want to look at the data like this tabulate the data present the data very nice 
you can see what's going on you can see what a nightmare this is for your data 
entry by looking and explaining to 
somebody how you would enter these data in that format because that only works 
if you've got one measurement but in the real world we have here we have one 
two three four five six measurements are you going to enter them on six 
different sheets it's all getting messy this is very simple and if ever you 
want to transform your data and get the total it just becomes another column 
down here 
sf0668: why doesn't he have repeated measurements of so many different factors 
nm0658: if you've got repea-, lots of repeated measurements they still keep 
going across 
sf0668: 
nm0658: and you might have sets of repeated measurements you might measure lots 
of things after twenty days another set of things after thirty another set of 
things after forty they can go across so you can go way across here er 
sm0669: what if experiment where you take in data from de-, for instance you do 
maize and pea or whatever it is and then you have all similar columns like this 
will it make safe to try to box them together or have separate because on them 
really i mean they're independent 
nm0658: okay 
sm0669: sort of shoot up into for say maize height 
nm0658: okay 
sm0669: 
nm0658: right th-, we'll that can be the last question before we have a quick 
break 'cause you have such a nice new coffee place downstairs er th-, er the 
question i hope it's understood to everybody there are some experiments which 
are called mixed cropping experiments 
does anybody not know what is a mixed cropping experiment you you all happy 
that this is a an experiment where you might have maize on sub-, some plots and 
beans on other plots and then the aim of the experiment is to see how the maize 
and the beans mix together so some plots have both maize and beans together and 
my simple rule for this is please stay simple so that is that please do exactly 
the same down here you have all your plots your treatments will say is it maize 
sole or bean sole or a mixture and then here are all your measurements and in 
your measurements you will have lots of blanks for the observations that don't 
the maize observations don't have any beans leave it blank or put it as missing 
it doesn't matter keep life simple in the past there has been a problem 
particularly related to a package called Mstat that is very poor at data 
manipulation and that has caused people to say well maybe i'll enter the maize 
data in one file and the bean data in 
another file or maybe i'll enter the maize sole data in one file and the bean 
sole data in another and the mixed data in a third and then they get very 
confused er so to avoid all that confusion keep my simple message don't confuse 
the entry with the analysis the reason people choose the different files is to 
simplify the analysis simplify the analysis afterwards but for the entry the 
entry is simple if you say how many plots did i have and i will enter 
observations and if there are some observations i don't have they're like 
missing values the reason is different but you just leave it blank or you put a 
missing value code in let's have a nice simple life and then you will find that 
the analysis is also simple after the break er we'll look at how to manipulate 
the data and then quickly on to repeated measures okay we'll have a break 
nm0658: 
i'm realizing as usual that luckily you have the slides for everything because 
i don't think i'm going to finish yet again and i do want to discuss repeated 
measures so i may have to leave out a little bit of one of the topics on data 
management i just want quickly to review the ideas to compare these two formats 
you've seen our recommended way of data entry this is all revision now has one 
row for each plot or unit and that's the lowest possible level if it's a 
subplot it's one row for each subplot so in the example in lecture three there 
are twenty-seven rows because there were three reps by nine treatments there 
were twenty-seven plots in the randomized one just now there were ninety-six 
rows because there were ninety-six plots therefore there's one column for each 
measurement the other way looks like a textbook example for a hand analysis 
also unfortunately and they've been written too 
many times but because they're all powerful they don't have to listen to 
anybody er in Excel it's the way you need to lay out the data for Excel to do 
an analysis of variance we do not recommend you use analysis of variance in 
Excel if you're going to do analysis of variance use it in Genstat or Minitab 
or anything but Excel's analysis of variance is not very good 
sf0674: statistically it's not very good 
nm0658: it's it doesn't do enough it doesn't show you residuals 
sf0674: 
nm0658: it doesn't encourage a critical looking at data it only goes up to two 
level factorials and it's much better if you're going to use Excel for your 
statistical analysis you go up to simple description and tabulation maybe you 
do graphics in Excel but don't get into ANOVA and regression in Excel you've 
gone off the end of Excel use the proper tool for the task you have when you 
have complicated analyses of data there are many statistics packages use the 
one that's most appropriate for you i think for experimental data it's 
absolutely clear that 
Genstat is the most appropriate but the important thing is that you use one 
that is appropriate and you've fallen off the end of a very general purpose 
tool which is a spreadsheet [cough] so as i've said before this lecture try to 
use the standard format for your entry it will save time on the analysis later 
but if somebody has entered the data differently it's usually quicker to 
reorganize the data than to have to retype so don't say oh gosh you've made a 
big mistake you'd better start again use the computer to help reorganize the 
data use either a statistics package or a spreadsheet i find that Genstat the 
competition between Genstat and Excel for reorganizing the data for you would 
be quite a good one because i think for reorganizing if you knew neither 
package it would be quicker to learn and use Genstat because it's built to do 
that sort of reorganizing than to use Excel but life is not equal most of you 
know Excel very well and you hardly know Genstat so some of you will 
prefer to reorganize your data in Excel and other people would prefer to learn 
a bit more of Genstat to do the reorganizing you should choose the method 
that's most appropriate for you and that will depend on your work in the future 
but if you're thinking of using Genstat seriously in the future then try and 
learn a bit about its methods for data manipulation and i'll show you a little 
bit about what that means first you have to understand what you're trying to do 
here is an example where i've taken the one from before where i assume we've 
entered the data in the wrong way and we want to go from this way to this way 
that's the way we would have had if we'd entered it correctly with the 
replicates and the treatments and the dry matter so you ought to see what it is 
we are trying to do we want to go i've said from this wide format to the long 
format we are trying to take these and i think you can see i hope you can see 
we're trying to stack these one below another 
so what goes across becomes stacked it's not er only that you could picture 
that's very easy in Excel but we want to do a little more than that because we 
want to take this which are already in the right form and we want to repeat 
that so this one on the left hand side gets repeated three times once for each 
column so it stays opposite not just this measurement but this measurement and 
these reps one two and three we want to have a new column called rep which goes 
one two three so it's not just stacking it's a bit more what do we mean in 
practice usually you want to stack the measurements and you want to carry the 
factors let's have a look at how that works in Genstat Genstat has a dialogue 
called stack you just have to go you should be getting to the stage with 
Genstat that you become curious and you think well there must be there 
somewhere and you go to spread manipulate and you will find stack within stack 
it will say how many columns do you want to 
stack together well it should be quite easy for you to say i want three columns 
because i have rep one rep two rep three i want those stacked one below the 
other i want to record the column source i want to record where they came from 
in a column called rep that's a new column and then you put your observations 
which were called rep one rep two rep three which were actually the yields and 
you put them there you notice it puts a one beside to say they're all going to 
be one column you might have had more things as well and then it would have 
twos beside because that would now be a second column and you have a repeat 
column which is treat you want treat to be repeated each time that's what we 
said was needed and when you click on okay then you will find that it will 
produce exactly that spreadsheet so it will take that and produce that i don't 
think that's too difficult so that is stacking in Genstat once you've got that 
far and you realize that's quite easy i just 
occasionally you want to go the other way round not often but sometimes you 
have it long and you want to go wide and if you ever need that there is you 
should now not be surprised if there's a stack dialogue there is also an 
unstack and this is like stacking things on a shelf you you can either stack 
them up or you can take them from there and you move them sideways so that 
they're now unstacked so that also exists that is one sort of data manipulation 
the second one i'm going to mention that it exists and then leave it because i 
think there is no not time for the repeated measures so let me just mention 
that the next it's in your notes that the next is that you sometimes have data 
at two levels and you must summarize one level to move it to another level the 
example that you have in the notes is data that were measured yields were 
measured on the plot level but tuber number was measured on the plant level and 
you want to summarize the tuber number 
onto the plot level to analyse with your other data and you'll be doing that in 
the practical one of the examples does that and that is called data summary 
before the analysis and that's very common and is usually where measurements 
are made at a lower level than the one where the treatments were applied so 
here the varieties were applied at the plot level but you measured something on 
plants within the same plot and so i just give you the three examples that 
you've had already in session three there were tuber measurements on twenty 
plants in each plot in session in the last session you had tree measurements 
this was what namex described on four trees in each plot so you have a plot was 
four trees and you measured the girth and other measurements on each tree 
within the plot but you want to analyse at the plot level because that's where 
you applied your treatments and in the Genstat guide the very simple example 
that you will have seen in the 
first part of the guide had four replicates and three treatments and there were 
twelve pens but there were two sections to each pen and that's the example in 
the Genstat guide so there we have twelve plots and two sections in a pen so we 
have twenty-four sections and we want to summarize from the twenty-four up to 
the twelve now i've put at the bottom check you recognize these these three as 
the same problem because in the Genstat guide we show you in detail how to 
solve this problem you will meet it very often and if you recognize that this 
is the same problem as this and this and many others then you can use Genstat 
to do that initial summary and let me just show you the the dialogue that you 
get with Genstat without giving you there's your data at your low level you 
want to get the total or the mean at the higher level and you want to carry 
other things along so your analysis can proceed at the higher level and so 
again you should find there is a summarize the 
spreadsheet which is another dialogue which will help you when you've got very 
detailed data at one level and you want to move up to another level so that's 
in your notes and it'll be in the practical does anybody have any i haven't 
covered it because i'm a little behind and i would like to tackle the repeated 
measures does anybody have any comments or questions on that yes 
sm0675: case we have er four trees er in each plot we know for example the 
directional reach of the trees 
nm0658: yes 
sm0675: so we wanted to know the production for the block separately then we 
add all the production of the four trees and then er we'd like to know er for 
the whole plot 
nm0658: that's correct that that that's very common er you you don't have to 
and in the notes we describe you can do the analysis at the tree level but you 
must accept that you applied your treatment at the plot level so the usual 
thing is to say what was the production for the whole plot and then you must 
say well do i want the mean production per tree or the total production and 
that depends on the problem 
on er some experiments i analysed er on disease there were measurements a an an 
insecticide was applied at the whole plot and then ten plants were measured to 
see how diseased they were and the idea was now for each plot you wanted a 
measure of disease in the olden days people always used the mean disease score 
as a measure of the disease per plot we decided that because we wanted to see 
the most effective insecticide we should also calculate the maximum disease 
score namely the disease score of the worst plant in the plot as a summary 
number to say that characterizes the worst that could possib-, if that worst is 
pretty good it's a good insecticide so it's not always usually you have the 
total or the mean in the plot but it can be the maximum or the minimum that is 
also useful so you calculate a summary statistic for the plot which you then 
analyse at the plot level last subject repeated measures these are very common 
in designed 
experiments where measurements are repeated on the same unit they can be in 
time or in space and the problem from a statistical point of view is the same 
so animals weighed each week would be i'm assuming the animal receives a 
particular treatment at the beginning of the experiment or has having a diet as 
you go through the experiment and is weighed each week so rather than just an 
ordinary yield experiment where you measure just once at the end you record 
successively in time that is a repeated measure in time most repeated measures 
are measures in time occasionally here's another example tree diameter is 
recorded every six months to see about the growth in human experiments you 
often do lots of measurements in time you measure the weight of babies every 
month for a year you measure the effectiveness of a treatment for cancer by 
recording every three months the effect on patients and so on so this is very 
common in many fields of application just 
occasionally these repeated measures are in space an example would be if you 
have a hedge and you want to see the effect of the hedge on the plants that are 
close to the hedge you might have a hedge er with a certain tree species and 
then you have some rows of maize which grow and you have six rows going away 
from the hedge and now you want to measure each row so you applied your plot 
consists of your hedge with six rows each side and now you want to repeat the 
measurement namely the yield but not for the whole plot but for each row to see 
the effect in space as you go further away from the hedge and that is a problem 
of repeated measures in space those repeated measures introduce problems of 
data management and analysis which we're going to look at and it reviews many 
of the ideas from this part of the course we'll have a very simple example and 
so you have more information it's in the Genstat guide there are five 
replicates this is an example for you because 
it's example where there are no blocks one or two er so there are just fifteen 
petri dishes little dishes and there are three isolates of a fungus and they're 
repeated five times but there's no group of five here group of five here there 
are just fifteen of them and there were six measurements made on days three 
four five six seven and eight [cough] how many plots how many measurements is 
it clear about the normal data and how many plots how many plots easy question 
fifteeen 
sm0676: fifteen 
nm0658: it is i'm sorry you you probably were confused 'cause it's too easy er 
it depends whether you think of your your confuse your measurements with your 
plots you see if you don't it should be obvious you have a question 
sf0677: destructive measurements on the same plot as the 
nm0658: the des-, tha-, that's a very good question when you are measuring on 
the same plot you have the choice of measuring let's say height which is 
something you can go back to exactly the same plant and measure or harvesting a 
few plants in the plot from a stats point of 
view it's roughly the same thing because they are they're still within the same 
plot but from a precision point of view it's much better if you can i-, i-, it 
isn't quite the same because if you go back to the same plant then your 
repeated measure is at the level plant if you're measuring the height whereas 
if it's destructive and you're measuring let's say the height of four plants 
and then you throw them away then and you measure the height of four more 
plants then you're still repeating the measure but the level is the plot level 
not the plant level because you can't go back to the same plant because it's 
harvested so where it differs is the level at which you're able to do the 
repeat usually we find that the lower the level you can do the repeat the 
better it is so we often find that non-destructive measurements are 
tremendously useful and last week i was examining somebody whose thesis is on 
taking aerial photographs of plots where you can measure the the area 
roughly of each plant repeatedly very very easily by taking a photograph and 
that is non-destructive and was shown to be a very good way compared to these 
small harvests that people often take where you get exactly what you want 
namely the harvest but it destroys it so you can't measure the same plants 
later on here's the data well sorry er i haven't i'd asked you how many plots 
there are but it hasn't answered you should be saying there are six 
measurements so that's six columns the fact they're on days three four five six 
seven eight doesn't affect and there are fifteen plots therefore i'm going to 
have fifteen rows of data and so the data are going to look well here's an 
example of the way the data could look where there's the unit there's the 
isolate there's the rep and there's my measurements on day three four five six 
seven eight [cough] now you now have to think of your strategy for the analysis 
and here we begin with a slight problem that is i would like you to 
look constructively at the data exploratory analysis we said is very important 
i wonder how you would like to explore these data well a very common way that 
people would like to explore the data is to see what's the change in 
observation over time sort of notice this goes on the first petri dish i go 
three-point-seven five six-point-one seven-point-five eight-point-three nine-
point-ei seem to going up with time to understand my data maybe it would be 
nice to look at that sort of graph as a function of time that would be a nice 
exploratory method but unfortunately for a stats package exploration works best 
on columns so you may wish to do that exploration in Excel or you will find 
Genstat helps so a strategy for the analysis nothing changes you've changed the 
problem but you haven't changed the strategy which is please start by looking 
critically at your data so start with data exploration and that's usually 
graphs so you look at all the data are there any odd 
observations you could do those Excel or in Genstat and you could get one graph 
for each plot so there'd be fifteen graphs be one way of exploring the data 
let's have a look at that first i'll come back to that for the second part so 
there's a way in Genstat of exploring the data and you will find that Genstat 
has a little menu which puts this out automatically so here's the graphs for er 
one treatment the second treatment and the third treatment and here is the 
graph for the means for the three treatments so there's a bit of analysis but 
here we have all our data this is the ninety observations there are fifteen 
lines because we have fifteen plots and each line has six points because we 
have six time points so we actually have all our data here and we could see if 
there was some odd observations i don't see anything particularly odd 
sm0678: when you say odd what exactly do you mean 
nm0658: the full set of numbers consists here's all our data these are all the 
numbers and what we have is we have 
fifteen plots so we're actually using all the numbers in those graphs you can 
see every number somewhere there so we're using all our data in producing those 
plots 
sm0678: my question is by looking at the graphs what are we looking for 
nm0658: er okay does anybody have anything they've found without knowing 
seriously what they're looking for 
sm0679: there is a 
nm0658: any impressions 
sm0679: increase er to an X -axis and 
nm0658: there seems to be an increase any er re-, remember your chick 
experiment and the increases sort of straight lines or curves 
sm0680: curves 
sm0681: curves 
nm0658: curves we we sort of like that 
sm0682: yes 
nm0658: or wiggeldy 
sf0683: some of them 
sm0682: mm some of them were 
sf0683: and some were straight mm 
nm0658: i don't notice any that go sort of right like that sort of starting 
going up to the top and coming down remember we're worrying about statistics 
there's variation so th-, everything you can't have things that are exactly 
straight 'cause we're just connecting the points do you do you think that for 
some of these it would be sensible to have a straight line model would that be 
a rough reasonable summary 
sm0684: 
nm0658: for all the plots are there any plots where you think a straight line 
model isn't going to be sensible i don't actually see many which is surprising 
usually you find maybe one treatment is curved and the other treatments are 
straight as you found with the barley and the wheat one was more curved than 
another you might want to recognize that does anybody see any very surprising 
observations i don't i don't i don't sort of see a sudden spike like this which 
might be a recording error so this is exploration and exploration can be 
positive or negative usually i find you notice one or two very odd observations 
here i don't see anything very odd and things seem to be increasing so that 
here where this is the mean of that one i feel reasonable confidence that 
drawing a straight line which is the average for those points is probably a 
reasonable summary and i notice now that this straight line so this is analysis 
and this 
is just presentation of the raw data and i now notice in this summary that 
these all three seem to be going up but this maybe is going up more gradually A 
it's lower and it's going up more gradually so from these i feel that this is 
probably a fair summary of the data i don't see any reason to say oh gosh it's 
not fair because of this and in here i'm starting my analysis and i've done 
that in a very simple way and visually does that help to answer your question 
[cough] okay so we have our data and i was looking for the strategy okay so i 
suggest for all analyses you start with a simple summary and then you go on to 
simple analyses what could the simple analyses be well here we have the data 
one simple analysis could be to analyse the data on day three just take one 
time point another one day eight so there's a very simple analysis you could 
analyse each of your observations separately the next simple analysis could be 
to take a useful summary one summary might be the difference between 
day eight and day three has the change been the same for each treatment and 
each replicate so that's what we suggest i keep losing the er so i've suggested 
the first simple analysis could be the data at each time point then we could 
have simple function like the final minus the initial or we could have the 
slope of each line now you don't want the slope if too many lines could be very 
curved but here i think getting the slope of each line might be a sensible 
summary as a strategy what sort of strategy is this well i would claim that the 
repeated measures are like observations at a lower level they're not exactly 
the same but they're a little like a split plot analysis they're like taking 
day as a level within a petri dish and then in this example we have six 
observations within each petri dish for the six days or we have ten weights 
within each animal so it's a little like a split plot experiment where the 
factor time is within the treatment just as an 
ordinary split plot but it's not quite a split plot because we don't randomize 
the times we can't like anything like that the analysis will be simpler if we 
first get a summary value at the plot level so our analysis is going to be 
simple if we summarize up to the petri dish whatever we do we've got fifteen 
petri dishes whatever summary we'd like to get that would be a simple analysis 
if we can go you were asking about split plots and i was saying simple 
experiments are at one level well repeated measures bring in a second level 
there are many methods for analysing repeated measures bringing in the two 
levels but the simplest is not to have two levels but is to summarize the data 
from the repeated measures up to the one level because that's where we apply 
the treatment which summary is appropriate depends on the data and the 
objectives and the booklet on analysis that i gave out in week eleven gives you 
some more details so the graphical display indicates that 
a useful summary might be the slope of the regression line for each petri dish 
so we then have a problem how do we get the fifteen slopes in Excel we could 
use the data as they stand in Genstat be better to stack the data so now to do 
those slopes because Genstat works with columns be better to stack the data and 
that was shown earlier and once you analyse with the stack data you will find 
and the way we'd go through that and get the regression you will find that here 
are the fifteen observations and here are the fifteen slopes and here is the 
analysis where we're actually analysing the slopes we're getting the individual 
slopes and there's fourteen degrees of freedom here because there's fifteen 
petri dishes and we find that er the effect of slope is statistically 
significant and these are the three slopes which are the lin-, the slopes of 
those three lines and we find that these first two treatments are about the 
same but this slope is rather flatter there 
are many other methods of analysis of repeated measures and Genstat has a whole 
set of dialogues specially for that they all try and get more levels more 
information by leaving the data at the two levels rather than summarizing up to 
one level they're often attractive in principle they're needed that should be 
an if they're needed if there is not enough data but to me they have a major 
problem that they are much more complicated and often their real problem is you 
can't tailor the analysis to the precise objectives of your research so they're 
like many complicated analyses that they're wonderful in principle but in 
practice they don't help that they are playing with data often and my 
conclusion is use the simple methods wherever possible and if you do use the 
more complex methods which you can because Genstat provides them from menus 
then don't just use them make sure they add constructively to what you were 
able to do quite simply with the simple methods okay practical work 
the practical follows the topics covered in this session so it's useful for you 
to review those so we're doing some on designing some on managing data and some 
on repeated measures in each case i've deliberately used examples from the 
Genstat guides so you don't have to finish just concentrate on those parts you 
find most interesting and that will help you get more experience in using 
Genstat and two final slides this is now the end of the five sessions which are 
specifically for the analysis of experimental data you now should have two 
things the first is the broad picture of the role of statistics in research 
projects which has come from sessions one to five that was last term so you 
should have an idea of how you use statistics in design in data management you 
should have 
reviewed basic statistical techniques statistical inference ANOVA simple 
regression that was the second part last term now you should be familiar with 
some of the special methods for analysing experimental data and hopefully you 
are therefore ready for a brief introduction to the role of modern statistical 
methods to help you in processing your research data the lecture room next week 
is the plant sciences lecture room so we're not here next week we're together 
with the other group in plant sciences 
ss: 
nm0658: in 
ss: 
nm0658: sorry 
ss: 
nm0658: the ground floor i pres-, the ground floor lecture room in plant 
sciences 
sm0685: you mean the small lecture theatre 
sm0686: there's one 
nm0658: i hope not it's w-, 
sf0687: there's one lecture theatre anyway isn't it 
nm0658: sorry 
sf0687: just one there isn't it 
nm0658: there's just one one lecture 
theatre i've been told it's got to take seventy of us 
sf0687: no it's large 
sm0688: 
nm0658: so it's the large lecture theatre 
ss: 
nm0658: and next week the practical is again for you in the Met department 
sm0689: is it just for us or will it be everybody else here as well 
nm0658: everybody is in the lecture and the practical is still split into the 
two groups as you go can you please we want your critical review of these five 
lectures and so we have another of the evaluations this is on this session any 
comments remember we've changed the course a lot this year so any comments they 
don't have to be polite and i'll collect this in the practical so can you take 
one as you go out and then i'll collect these in the practical