· Q. 1. I need to compare the national average depression score in elderly patients (n=3000+) with the depression score of my small group of patients (n < 16). Is there a specific test I can use to see if the patients represented in my data are significantly more depressed, considering the the small sample size I have?

A. This answer assumes you are using the statistical package SPSS.  However, if need be, please feel free to improvise! It is best not to compare the reference population with your sample as though they were two samples. Instead, it would make sense to perform a one-sample t-test with your sample data prepared in an SPSS spreadsheet.  I would recommend that you don’t decide in advance that you are looking for an increase in mean, but that you perform a two-sided (or, two-tailed) test, which just tests for a difference. This is a tougher test and less susceptible to picking up a difference due to chance. (You can do a one-tailed test, however, if (prior to seeing your sample mean) you had every reason to believe it would be higher than the population mean and that to believe anything else would not have made sense.)   To further enhance your findings, you should consider constructing a confidence interval for the difference between your sample mean and the population mean.

In carrying out the above steps, you are assuming that your data already satisfy the Normality conditions for the one-sample t-test. Have you checked that they do?

All of these areas are covered very well by means of the resource One sample t-test. (In the table on p. 3, ‘Lower’ and ‘Upper’ refer to the bounds of the above confidence interval. The results can be expressed as “the mean difference (sample mean – population mean) was 26.86 (95% CI: (11.27, 42.46), p = 0.002))”.

 To reinforce your learning, you may also wish to conisder the tutorial in the movie 1 sample t-test and use the practise data to help you interact more effectively with the tutorial.

· Q 2. Are there alternatives to the one sample t-test for data which exhibit a considerable degree of non-Normality?

A. If the data are highly skewed to the right or are exponentially distributed, you should try a log transformation of the data (either to the base e or the base 10) or squaring the individual data values. If the transformed data is Normally distributed, you should perform a one-sample t-test on this data but be careful with the interpretation of the results.

Failing the above, you should consider the one-sample sign test or one-sample Wilcoxon signed rank test. Both of these tests are very straightforward to carry out using the statistical software package Minitab. They are also discussed under Topic 19 of of the electronic version of the book Medical Statistics at a Glance.

If you are registered with the University of Edinburgh, you can consult the electronic version of this book via the University’s library discovery system, DiscoverEd.

Here are some reference details:

• Title: Medical statistics at a glance
• Author: Aviva Petrie
• Caroline Sabin
• Publisher: Hoboken : Wiley
• Publication Date: 2013
• Edition: Third edition

· Q 3. I have some survival time data for three categories of patient defined by their ISS risk score (1, 2 or 3).  For each of these categories, I also have a single predicted median survival time. I would like to perform a test for each category to see if the median survival time for my sample differs significantly from the predicted median. Which test should I use and which statistical package?

A.  Here, your categories represent 3 groups and you wish to test the null hypotheses

Actual median for group 1  = predicted median for group 1
Actual median for group 2  = predicted median for group 2
Actual median for group 3  = predicted median for group 3

You should read the data into Minitab and perform the one-sample sign test on the median. You can read your data from Excel into Minitab for this purpose.

To obtain explicit advice on this test (including a worked example with sample data and advice on obtaining a confidence interval for the median), when in Minitab, go to the menu Stat, select ‘Nonparametrics’ followed by ‘1-Sample Sign’ and then click the button ‘Help’.

Please note, that you should perform the above test separately for each of the above null hypotheses.

Hypothesis Tests for a Single Group of Continuous Data by Margaret MacDougall is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.