The Mood’s Median test is a hypothesis test used to determine if there is a significant difference between two or more independent groups.
This test is also known as the Wilcoxon-Mann-Whitney test. The test is named after John Wilder Tukey, Frederick Mosteller, and Herman Chernoff. It is used to compare two unpaired groups.
This test is non-parametric and does not assume that the data comes from a normal distribution. The test can be used with ordinal or interval data. The median is used as a measure of central tendency for this test. This test is also robust against outliers.
The null hypothesis for this test is that there is no difference between the two groups. The alternative hypothesis is that there is a difference between the two groups.
This test can be used when there are more than two groups, but pairwise comparisons must be made between the groups. This can increase the chances of a Type I error. Bonferroni correction can be used to control for this error.
How the Mood’s Median Test Works
The Mood’s Median test ranks the values from lowest to highest and then calculates the median for each group. The median for Group 1 (M1) is calculated by taking the average of the two middle values if there are an even number of values in the group. If there are an odd number of values, then the middle value is taken as the median. The median for Group 2 (M2)is calculated similarly.
The difference between M1 and M2 (D) is then calculated. If D = 0, then H0 is true and there is no significant difference between the two groups. If D≠0, then H1is true, and there is a significant difference between the two groups.
To calculate the p-value, we use the formula: p-value = P(X≤D), where X ∼ N(0,1). If the p-value is less than 0.05, then we reject H0 and conclude that there IS a significant difference between the two groups at α= 0.05.
How to Perform the Mood’s Median Test
The Mood’s Median Test can be performed using Excel or Minitab. For this example, we will use Minitab.
First, you need to enter your data into Minitab. You can do this by either typing in your data or importing it from an Excel file. Once your data is entered, go to Stat > Nonparametrics > 2 Related Samples > Medians/Mann-Whitney…
Next, you need to select your response variable and your grouping variable. The response variable is the variable that you are measuring. The grouping variable is the variable that determines which group the observation belongs to. In this example, we will use height as our response variable and gender as our grouping variable.
Please note that you need to have at least two observations per group in order to perform this test.
Once you have selected your variables, click OK and Minitab will generate a report containing your results.
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Interpreting the Results of the Mood’s Median Test
The Mood’s Median Test results are interpreted similarly to other hypothesis tests such as the t-test and ANOVA. The results will contain information about the p-value and significance level. The p-value helps you determine whether there is a significant difference between the two groups. A p-value of less than 0.05 indicates that there is a significant difference between the two groups at a 95% confidence level. This means that if you were to repeat this experiment 100 times, 95 times out of 100 you would get a result that was at least as extreme as what was observed in this experiment if there was no difference between groups.. In other words, if there was no difference between groups, you would only expect a result this extreme 5% of the time by chance alone.
Therefore, you would conclude that there is a difference between groups. If the p-value were more significant than 0.,05, then you would not conclude that there was a significant difference between groups. Instead, you would say there was not enough evidence to support such a claim.
For there to be enough evidence to conclude that there was indeed a difference between groups,.the p-value must be less than 0.,05. In other words, the results must be statistically significant at a 95% confidence level.
Conclusion:
In conclusion, Mood’s Median Test is a statistical test that can be used to determine if there is a significant difference between two or more independent groups. This test does not assume that data comes from a normal distribution, and it can be used with ordinal or interval data sets.
This test calculates medians to compare unpaired groups. Finally, this tests robust against outliers which makes it a powerful tool when analysing data sets with potential outliers present.
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