Worked example for Mann Whitney U test for A2 Geography students

1. Comparing medians: the Man Whitney U-test The Mann Whitney U-test is a fairly complicated statistical test to understand, though it is quite easy to apply to a set of data. So, while the calculation is relatively easy, knowing when to apply it, and what the calculation actually means, is a little more difficult. It is also important not to be put off by the formula.

3. Though this is a nonparametric statistical test, both samples should have a similar distribution. You can plot the data for each set on a simple graph to check this. Like many of the other statistical tests, you have to start with a null hypothesis (H o). However, unlike some of the other tests, the null hypothesis (H o) is always the same: There is no significant difference between the two samples.

4. Applying the Mann Whitney U-test Comparing two traffic flows in a town centre A student was interested in finding out if a new retail development had an impact upon traffic (and therefore congestion) in the local area near to the development. There were two parts to the primary data collection. The first part was conducted before the construction of the planned development (sample x). Methodology for primary data collection She recorded the time of day and date. She counted traffic (in both directions) on 10 streets around the development selected randomly). She counted for 10 minutes. She used a stopwatch for timing and a simple tally chart for recording the data. She completed the tally at different times of the day. TIP Is it a one-tailed or a two-tailed test? This relates to the difference between the data sets. If you assume one specified data set will be larger than the other, you are investigating a one-tailed distribution. If you assume differences can operate in both directions, i.e. up or down, you are investigating a two-tailed distribution. This is important when you interpret you findings using the critical values. In this example, the student is assuming traffic can go up or down in study 2 for all sites, despite the fact that more customers are likely to be attracted to the development. In this case, this makes it a two-tailed test

5. For the second study (sample y), she waited until 2 months after the development had been completed. She went to another 10 sites (selected randomly) and repeated the test. She then devised the following null hypothesis (H ₒ): ‘ There is no significant difference in traffic flows before and after the development.’ Now let’s take a look at the formula: U ₓ = Nₓ.N ᵧ + N ₓ(Nₓ + 1) 2 - Σ rₓ U ₓ is the Mann Whitney calculation for sample x n is the number in the sample Σ rₓ is the sum of ranks for sample x (‘sum of’ just means added together)

6. The best way to proceed is to incorporate the findings into a table that also allows you to calculate the result. When you get two or more equal values, use the mean rank. Here are the student’s findings: Complete the table by ranking all the data from highest to lowest. Total traffic flow in 10 minutes ( ₓ ) Rank r ₓ Site Number Total traffic flow in 10 minutes ( ᵧ ) Rank r ᵧ 126 11 1 194 148 7 2 128 85 15.5 3 69 61 19 4 135 179 4 5 171 93 12.5 6 149 45 20 7 89 189 3 8 248 1 85 15.5 9 79 93 12.5 10 137