Mann Whitney U test

When carrying out the internal assessment, nothing seems to worry students (and teachers) more than the application of inferential statistics. And yet – it is actually not as difficult as it may seem.

The Mann Whitney U test is used when we have an **independent samples design**. Even though I may have **interval or ratio data in my results, the test will convert my data to ordinal in order to carry out the test**. This means that part of the test (which we will not have to do manually!) determines the rank of each piece of data within the sample. We do this because we tend to have small sample sizes for IB Psychology IA’s and because often we do not have a standard distribution of data – but rather, the data tends to contain outliers.

When we calculate the Mann Whitney U – we get a "U" value. We then have to determine whether the U value is "significant" or not. The concept of significance is simply – what is the probability that my results are only due to chance?

When we discuss probability, psychologists look for a maximum probability of .05 that the results are due only to chance. In other words, I want to be able to say with a 95% level of confidence that my results are **not** due to chance. The typical "p values" are p < 0.05, 0.25 and .01.

The U value is always compared to a "critical value." The idea of critical values is demonstrated in the graph below.

This diagram demonstrates what happens with a one-tailed hypothesis. Let’s say that my hypothesis is that "Noise will increase the number of words that an individual will be able to memorize from a list of 30 words." If the value for U that I get is in the "white" area of the graph under the curve, then we can say that my results were simply due to chance. If that is the case, then I have to "retain the null hypothesis" – it would appear that noise does not have any effect on the number of words that an individual will be able to memorize from a list of 30 words.

However, if my U value falls into the striped area under the curve, then I know that it has met or exceeded the critical value (t) and thus I can reject my null hypothesis at p < 0.05 – or whichever value t represents.

One program that helps us to calculate U values is **Vasserstats.net** The following screencast will demonstrate how to use this simple online program.