Data handling assignment

Data Handling – Assignment

T-test and Power Analysis for an experiment with mice.

You are using mice as a model organism to study the correlation between nutrition, obesity and diabetes. Recently, you completed an experiment, in which you kept 6 mice on a normal chow diet and another 6 mice on a High Fat Diet (HFD) for 10 weeks. Your body weight data show that the mice on HFD have gained much more weight than those on chow. But, you are also interested in analysing the impact of HFD on blood glucose levels and glucose metabolism. Therefore, you decided to undertake a glucose tolerance test at the end of the 10 week period. Now you are examining your data for a significant difference between the two diets at each time point after glucose application to the mice. You are not interested in comparing the two time points.
These are your blood glucose data in mM concentrations:

20 min: 100 min:
Chow: HFD: Chow: HFD:
12.8 14.0 9.5 11.2
12.4 13.5 8.7 10.5
13.4 13.2 8.5 10.8
12.9 13.0 9.4 11.5
13.5 13.7 9.0 11.3
12.7 13.9 9.3 10.6

Use the programme ‘Excel’ to analyse the average values and the standard deviations for each group. Then, use the student’s t-test function, to analyse for a significant difference between chow and HFD at 20 min and at 100 min. Look up the Help? support in Excel, if you are uncertain how to use these functions (you should have used these before in other exercises).
For the t-test you have no pre-set assumption about which direction the blood glucose levels might change in the HFD group versus chow, i.e. whether they might be lower or higher. Furthermore, the variance in your two-group comparisons is similar.

1) What are the average blood glucose values and standard deviations for each group and time point? (2 marks)

2) What type of student’s t-test is applicable here: paired or independent, 1- or 2-tailed? (1 mark)

3) Briefly explain the general statistical terms “Null-hypothesis” and “Type I error or α-error probability”. (1 mark)

4) In your Excel t-test: Are the datasets between chow and HFD significantly different at 20 min and 100 min, respectively, if you tolerate a 5% probability level of falsely rejecting the Null-hypothesis? What is the probability (P-value) of your test for each time point? (2 marks)

Now that you have done your statistical test on the datasets, you still have doubts about the significance of the 20 min time point. You decide to carry out a Power analysis, to determine with what sensitivity you have detected the correct effect. Before you start…

5) Briefly explain how Power/Sensitivity in an Alternative Hypothesis scenario relates to the type I error rate α in the Null-Hypothesis scenario. (5 marks)

Go to http://biostat.mc.vanderbilt.edu/twiki/bin/view/Main/PowerSampleSize, the website of the Biostatistics Department of the Vanderbilt University (this software is also available to download from your University login via your Desktop – Install University Applications – Statistics folder – PS Power and Sample Size Calculation). Download and set-up the free Power and Sample Size Programme (pssetup3.exe); Windows and Mac versions available). Let me know, if you have problems with the download!
The programme can do such calculations for different types of statistics. Obviously, you will need the t-test tab. If you click on any of the blue links, a Help page will come up, providing further useful background explanations.

First, you want to find out what Power your experiment had. In other words: What level of certainty is associated with your t-test result. This takes into account the sample size and the standard deviations of your experiment.

In the programme, under ‘Output’ select the right option; also select the correct ‘Design’ used in your t-test (see question 2).

The programme does not accept percentage values; you have to type in absolute/decimal numbers. You need to use the same Type I error probability that you used for doing the t-test. δ refers to the difference between average values. Round the standard deviation to one decimal place.

6) What is the Power associated with the t-test result of your experiment at the 20 min and 100 min time points, respectively (in %)? Are you confident enough in your data to present them at a scientific meeting? (2 marks)

7) For your 20 min time point: What would be the Power, if the standard deviation were half the size of what you obtained? (0.5 marks)

8) How could you improve your dataset? (0.5 marks)

9) Finally, using the appropriate Output function of the programme, calculate how many mice you would need in each group, to obtain a 90% certainty (Power) of detecting a significant difference at the 20 min time point! Assume that the difference between average values and the standard deviations remain the same. (1 marks)

10) Now let’s see what sample sizes are recommended by the Resource Equation method (see lecture notes), and how they compare with those from the Power analysis. Undertake a Resource Equation calculation for the sample size that was used in the experiment, and another one with the sample size recommended by the Power analysis (certainty level 90%; question 9). Briefly explain what the individual variables of the equation stand for in this context. What E values do you get? Are these within the recommended range of the Resource Equation and are the two methods of sample size calculation in agreement? (6 marks)

11) Explain the concept of a ‘Randomised Block Design’. How could you apply it in this glucose tolerance experiment, if you cannot do the experiment with all mice at the same time? You need to balance two factors: a) the minimal number of mice that should generally be represented in one block, and b) how the blocks influence the Resource Equation outcome. Give an example for a block design of this experiment. How would you allocate the mice to a block and how many per block? Provide the accompanying Resource Equation calculation for your design with an E-value within the recommended range. N-numbers might have to be different from the above experiment. (6 marks)