Inferential Statistics

The purpose of inferential statistics is to see if there is any validity that can be drawn from your results.  The key idea is to see if your results are statistically significant.  Significance is the likelihood that a finding or a result is caused by something other than just chance. Usually, this is set at less than 5% probability (p< 0.05), meaning that the result is at least 95% likely to be accurate (or that this result would be produced by chance no more than 5% of the time).

Essentially, there are three tests that we tend to use. The justifications for choosing a test are based on several factors:

         What is the level of data? Nominal, ordinal, interval or ratio?

         What is the experimental design? Independent samples or repeated measures?

         Both sets of data should have similar variance? If not, then the highest level of analysis that can be used is at the ordinal level.

The following tests are the most frequently employed for the IB Psychology IA:

         For nominal data, the chi squared should be used for independent measures. A sign test should be used for repeated measures.

         For independent measures, the data is converted from interval or ratio to ordinal data and the Mann Whitney U Test is used. You do not convert the data to use the test - the data will be converted as part of the test.

         For repeated measures, a Wilcoxon Signed Ranks Test is used. Once again, the data is converted to ordinal.

Chi Squared Test

Mann Whitney U Test

Wilcoxon Signed Ranks Test


Key points for the Inferential statistical results

1. Include the printout from the calculations in the appendices. Be sure that the appendix has an appropriate title and that the printout is understandable.

2. Justify why the inferential test was chosen. This is based on design and level of data.

3. Make a statement of conclusion including a statement of significance. The statement of significance should include the critical values and the observed values. It should also state whether the null hypothesis is retained or rejectedSee below.


This is worth 3 marks out of 28 for HL.


Statements of significance


Students must determine whether the obtained value meets the critical value for significance and to what level.


A statement of significance should look like this:

The U value of ( x) does not meet the critical value of (y). Thus, the results are not significant and may be due to chance. The null hypothesis is retained. Therefore . . .

Here is where they then make the conclusion based on the aim of their study. For example - the null hypothesis is retained; therefore, the level of noise to which an individual is exposed to while reading a list of words has no effect on the number of words recalled.


The U value of (x) exceeds the critical value of (y). Thus, the null hypothesis is rejected and the research hypothesis is supported at p < 0.01. Therefore...

Here again is where they then make the conclusion based on the aim of their study. For example - the null hypothesis is rejected; therefore, we can conclude that higher levels of noise to which an individual is exposed to while reading a list of words decreases the number of words recalled.

Once Again.......

HL candidates must clearly state the conclusions that they can draw from inferential statistical analysis of their data. In addition to stating the results of descriptive statistics, HL candidates must:

         Identify the statistical test that was used.

         Justify the statistical test that was used - that is, explain why this test was chosen, and not a different test.

         State the mathematical results, making reference to calculations which should be relegated to an appendix.

         State the conclusion with regard to whether the null hypothesis is retained or rejected based on the results of the statistical test. The level of significance should be included in this conclusion.

A couple of samples of what the Inferential Paragraph should look like.