Important Questions for IGNOU MAPC MPC006 Exam with Main Points for Answer - Block 4 Unit 2 Mann Whitney ‘U’ Test for Two Sample Test

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Block 4 Unit 2 Mann Whitney ‘U’ Test for Two Sample Test

1) A researcher had an experimental group of m = 3 cases and a control group of n = 4 cases. The scores were as following:

Exprimental scores: 9, 11, 15
Control scores: 6, 8, 10, 13

i. In the above, Assume these groups are independent, apply appropriate statistics and state whether the experimental condition and control conditions differ or not.

Assuming the groups are independent, the Mann-Whitney U test is the appropriate statistic to apply. This test is the non-parametric equivalent of the independent samples t-test and is suitable for small sample sizes and when the data may not be normally distributed.

ii. In the above, Assume these groups are correlated, apply appropriate statistics and state whether the experimental condition and control conditions differ or not.

Assuming the groups are correlated, the Wilcoxon Matched Pair Signed Rank test is the appropriate statistic to apply. This test is the non-parametric equivalent of the paired samples t-test and is used for two repeated (or correlated) measures when measurement is at least ordinal.

2) Doctor Radical, a math instructor at Logarithm University, has two classes in advanced calculus. There are six students in Class 1 and seven students in Class 2. The instructor uses a programmed textbook in Class 1 and a conventional textbook in Class 2. At the end of the semester, in order to determine if the type of text employed influences student performance, Dr. Radical has another math instructor, Dr. Root, to rank the 13 students in the two classes with respect to math ability.

The rankings of the students in the two classes follow:

Class 1: 1, 3, 5, 7, 11, 13
Class 2: 2, 4, 6, 8, 9, 10, 12

(Assume the lower the rank the better the student).

To above, Apply appropriate statistics and tell if the type of text employed influenced students performance?

To determine if the type of textbook influenced student performance, the Mann-Whitney U test is appropriate. Although the data is in rank order, it originated from a continuous variable (math ability), and the groups are independent. The Mann-Whitney U test assesses if two independent samples come from identical populations.

3) Why should you not use the large-sample z-test version of a non-parametric test when you have samples small enough to allow the use of small sample version?

You should not use the large-sample z-test version of a non-parametric test with small samples because the small-sample version provides a more accurate result. The large-sample version relies on the normal approximation, which may not be reliable with small sample sizes. Using the small-sample version, which uses exact probabilities, ensures greater accuracy for smaller datasets.

4) Which non-parametric test should we use when the data is obtained from two different samples (Independent of each other) and we wish to see the difference between the two samples on a particular variable?

When you have data from two different, independent samples and want to see the difference between them on a particular variable, you should use the Mann-Whitney U test.The underlying assumption of the Mann-Whitney U test is that the two sets of scores are samples from the same population. Therefore, it is assumed that the two sets of scores do not systematically differ from each other due to random sampling. The test also assumes that the samples are independent of one another, the original variable is continuous, and the underlying distributions are identical in shape.

5) What is the underlying assumption of Mann-Whitney U test?

Various sources (e.g., Conover (1980, 1999), Daniel (1990), and Marascuilo and McSweeney (1977)) note that the Mann-Whitney U test is based on the following assumptions:

Each sample has been randomly selected from the population it represents;
The two samples are independent of one another;
The original variable observed (which is subsequently ranked) is a continuous random variable. In truth, this assumption, which is common to many nonparametric tests, is often not adhered to, in that such tests are often employed with a dependent variable which represents a discrete random variable; and
The underlying distributions from which the samples are derived are identical in shape. The shapes of the underlying population distributions, however, do not have to be normal.

6) What unit of sample is considered as an appropriate sample for Mann Whitney U test for small sample?

The Mann-Whitney U test is generally considered appropriate for small samples when each group has no more than 20 items.

7) What is the rationale of applying Z test be applied in a non-parametric setting?

While the Mann-Whitney U test is a non-parametric test, the Z test can be applied when the sample size is large enough (generally N > 20). In this case, the distribution of the U statistic approximates a normal distribution, allowing for the use of the Z test to assess statistical significance.

8) Which non-parametric test should we use when the data is obtained from two related sample and we wish to see the difference between the two samples on a particular variable?

When the data comes from two related samples and you want to observe the difference on a particular variable, you should use the Wilcoxon Matched Pair Signed Rank test.

9) Which one assumption does not apply to Wilcoxon Matched Pair Test, which applies to Mann Whitney U test?

The assumption that the two samples are independent of one another does not apply to the Wilcoxon Matched Pair Test, but it does apply to the Mann-Whitney U test. This is because the Wilcoxon test is specifically designed for related or paired samples, where the data points are connected.

10) What is the difference between t Test for Matched Pair sample and Wilcoxon Matched Pair Test?

The key difference between the t-test for matched pairs and the Wilcoxon Matched Pair Signed Rank test lies in their assumptions and data requirements.

The t-test is a parametric test that assumes the data is normally distributed and measured on an interval or ratio scale.
The Wilcoxon test is a non-parametric test that does not assume normality and can be used with ordinal data or when the normality assumption of the t-test is violated.

Essentially, the Wilcoxon test is a more robust alternative to the t-test when dealing with related samples and non-normal data distributions.

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