Session 9: Week 10.
Inferential Statistics II
In your previous lab class you will have learnt how to analyse parametric data taken from independent measures study designs and also, should the data transpire to be non-parametric in nature, you will now know how to conduct the appropriate non-parametric analyses.
This lab will extend these methods of analysis to cover repeated measures research designs, whereby the same individuals are tested on two occasions and therefore act as their own controls. This therefore allows us not only to compare the ‘average’ scores of each group but also to pair up individual data points to assess whether any difference between groups was consistent across all individuals.
Again, this lab is deliberately shorter than in previous weeks to provide you with an opportunity to address your coursework and seek assistance with any problems you may have.
TASK 1: The Pairedt-Test
A researcher plans a study to determine how effectively a new carbohydrate beverage can increase blood glucose concentrations following feeding. He therefore randomly samples 18 healthy young volunteers to take part in a one group pre-test post-test experimental design. This experiment requires participants to provide a resting blood sample before consuming 500 ml of the test solution and then having another blood sample taken 30 minutes later. The glucose concentrations measured in this blood (mmoll-1) can be accessed by clicking here. The hypothesis for this investigation is that ingesting the carbohydrate solution will increase blood glucose concentrations.
Importantly, you first need to assess the data for normality to determine whether parametric analyses are appropriate. However, given that statistical analysis of repeated-measures data focuses on the paired differences between treatments, it is not the raw ‘pre’ or ‘post’ values which need to be normally distributed but rather the paired differences between pre and post. You should therefore create a new column as you did in your first SPSS lab using the ‘TRANSFORM-COMPUTE’ function, by entering ‘diff’ as a target variable and then entering Post minus Pre.
Having assessed the normality of the difference scores you can now conclude that the mean is an appropriate measure of central tendency and can apply a parametric procedure to examine whether the mean increases significantly following carbohydrate ingestion. This is done using a Paired Samples t-test.
Based on the results of the above t-test, the researcher concludes that his hypothesis was correct. However, which threats to validity are able to operate within this researcher’s experimental design, i.e. is he justified in his conclusion that changes in blood glucose (DV) are entirely attributable to carbohydrate ingestion (IV)?
What addition to the experimental design would you recommend to the researcher to improve the study design?
SAVE YOUR WORK
Save the SPSS output relating to the pre-post difference for later reference.
The researcher agrees to take your advice and asks all the participants to return to his laboratory on a second occasion. This time, however, they are provided with 500 ml of flavoured water in between their two blood samples. Click hereto access an updated file which includes this new data (n.b. this second visit is labelled as Pre2 and Post2, you can ignore the RPE columns for the moment). What experimental design is now described?
You can now conduct a paired t-test in the same way as before but comparing Post with Post2. The researcher is now surprised to find that the mean blood glucose concentration following carbohydrate ingestion is not significantly different than that following ingestion of flavoured water. However, the hypothesis for this study was that carbohydrate ingestion would increase blood glucose, which infers that we must establish some change in the dependent variable. The above examination of Post versus Post2 actually reflects a static group comparison and therefore only provides information regarding current status (see lecture notes week 3).
To adequately address this research question, we must take into account each participant’s status before the IV was applied. Therefore, you need to repeat your earlier step via the ‘TRANSFORM-COMPUTE’ function to produce difference scores for the second measurements as well (i.e. create a ‘diff2’ column using the Pre2 and Post2 columns).
Before applying a paired samples t-test to these new data, you should run a quick test for normality to confirm that parametric analysis are still appropriate (again, for repeated-measures analyses it is not the raw ‘pre’, ‘post’ or even ‘difference’ columns that need to be examined but rather the paired differences, i.e. the differences in differences; ‘diff’ minus ‘diff2’). Having established that the data is normally distributed, you can now use a paired samples t-test to determine whether the increase in blood glucose was greater following carbohydrate ingestion than following ingestion of flavoured water.
Write down both a null and alternative hypothesis for this investigation and decide which one to accept and which to reject.
Why might the baseline glucose concentrations have been different between treatments and how might this bias be controlled for?
SAVE YOUR WORK
Save your SPSS outputs to your ‘H:\studyskills’ folder.
TASK 2: The Wilcoxon Matched-Pairs Test
As described above, repeated measures research designs result in matched pairs of data (i.e. we can identify which score in trial A corresponds with which point in trial B). However, you will now be aware that there are certain circumstances in which parametric methods such as t-tests are inappropriate. You will now be conducting the non-parametric equivalent of a paired t-test, the Wilcoxon Matched-Pairs Test.
Refer back to the data you have just analysed and you will see two additional columns labelled RPE and RPE2. The researcher from Task 1 extended the focus of his study to a more applied field by asking the participants to exercise on a cycle ergometer at a fixed workload immediately following their second blood samples. He then assessed their rating of perceived exertion using the visual scale shown here. In this way he hoped to establish whether the increase in blood glucose concentration elicited by the carbohydrate solution might also reduce the perceived effort of subsequent exercise.
You should be well aware by now that parametric analysis requires a normal distribution so you should test this RPE data for normality.
Before selecting our statistical test, we must also consider whether this data conforms to the other assumptions of parametric analyses. You should therefore refer back to the study design to determine whether the participants were randomly sampled. In addition, parametric analyses require data to be of at least the interval level of measurement, what level of measurement does the RPE scale represent? (you may need to amend the measure columnin variable view to reflect your choice)
Which of these three assumptions of parametric analyses have been violated (i.e. Normality, Sampling, LOM)?
You will need to assess the treatment differences in RPE using a Wilcoxon Matched-Pairs Test.
Based on the result of this test, would you conclude that pre-exercise carbohydrate ingestion reduced perceived effort?
You might like to conduct a quick t-test to see if the parametric and non-parametric statistics methods agree.
SAVE YOUR WORK