Wilcoxon for Independent Samples

Wilcoxon for Independent Samples. Practice questions to deepen understanding of the Wilcoxon test for independent samples. Online statistics practice with full solutions and step-by-step explanations.

Independent Wilcoxon practice — Mann-Whitney for independent samples, joint ranking, U computation. Detailed explanations.

30 questions

Question 1

3.33 pts

Question 1:
What does the Wilcoxon test for independent samples examine?

Tests whether the location (median) of two independent populations differs.

Tests whether the means differ.

Tests whether the values fit a normal distribution.

Tests whether the variances are equal.

Explanation:

The Wilcoxon test for independent samples (also called Mann Whitney) tests whether two groups differ in their central location without the assumption of normality.

Question 2

3.33 pts

Question 2:
When is it appropriate to use the Wilcoxon test for independent samples?

When the data are not normal or the measurement scale is ordinal.

When we have normal data and a large sample.

When the measurements are dependent.

When we have a two-way frequency table.

Explanation:

Wilcoxon is suitable for comparing two independent groups when normality cannot be assumed or when the data are not fully quantitative but rather ordinal.

Question 3

3.33 pts

Question 3:
What is the additional name for the Wilcoxon test for independent samples?

Mann Whitney U test

Chi Square test

Kolmogorov-Smirnov test

Paired t-test

Explanation:

The most common name is Mann Whitney U. It is a non-parametric test for comparing two independent groups.

Question 4

3.33 pts

Question 4:
What is the basic assumption of Wilcoxon for independent samples?

The two groups are independent of each other.

The two groups are symmetric.

The groups have equal variances.

The data are normally distributed.

Explanation:

The main requirement: complete independence between the groups. No need for normality or equal variances.

Question 5

3.33 pts

Question 5:
What is the test based on computationally?

Ranking all data from both groups together.

Calculating the mean of each group.

Calculating the standard deviation of each group.

Summing all the raw values.

Explanation:

The test ranks all the data from both groups together and is based on the sum of ranks of each group.

Question 6

3.33 pts

Question 6:
What is the null hypothesis in the Wilcoxon test for independent samples?

The two populations have identical location (central position).

The two populations differ in variance.

The two populations are normal.

The two populations are similar in their full distribution.

Explanation:

The null hypothesis: there is no difference in the central location between the two populations (the medians are equal).

Question 7

3.33 pts

Question 7:
What is the research hypothesis in the Wilcoxon test for independent samples?

There is a difference in central location between the two populations.

There is a difference in variances.

There is a linear relationship between the variables.

There is dependence between the measurements.

Explanation:

The researcher's hypothesis claims that the groups differ in their central location.

Question 8

3.33 pts

Question 8:
The figure shows two groups and the ranks they received. Which group probably has higher values?

Group B

Group A

there is no way to infer from the ranks

the two groups are identical

Explanation:

Higher ranks → higher values. Here group B has significantly higher ranks and therefore has higher values.

Question 9

3.33 pts

Question 9:
What is a common mistake regarding the Wilcoxon test for independent samples?

thinking it tests means instead of location or ranks

thinking it requires normality

thinking it requires dependent samples

thinking it cannot be used with small samples

Explanation:

Wilcoxon does not test means but rather the structure of location and ranks. It is particularly suitable when the mean is not a stable measure.

Question 10

3.33 pts

Question 10:
Why is Wilcoxon sometimes preferred over the t-test in small samples?

Because it does not assume normality of the values.

Because it always gives a low p.

Because it is suitable only for small values.

Because it allows mixing dependent and independent measurements.

Explanation:

In small samples it is hard to assume normality. Wilcoxon does not require normality and is therefore more suitable in such situations.

Question 11

3.33 pts

Question 11:
What are the main usage conditions for the Wilcoxon test for independent samples?

The two groups are independent and the measurement is at least ordinal.

The two groups must be normal.

The two groups must be equal in size.

The measurement must be on a ratio scale.

Explanation:

Wilcoxon is suitable when the groups are independent and the measurement data are at least ordinal. There is no requirement for normality and no requirement for equal sizes.

Question 12

3.33 pts

Question 12:
What is the U statistic in the Mann Whitney test based on?

On the sum of ranks of each group.

on the difference of means

On the variance of the larger group.

on a count of frequencies

Explanation:

The U statistic is based on the sum of ranks given to the values in each group after combined ranking of all the data.

Question 13

3.33 pts

Question 13:
What is the important information examined when comparing two groups in the Wilcoxon test?

Whether the ranks of the first group are significantly higher than the ranks of the second group or vice versa.

Whether the mean is larger.

Whether the standard deviation is higher.

Whether the distribution looks normal.

Explanation:

The comparison between the groups is done by examining the ranks. Higher ranks → larger values.

Question 14

3.33 pts

Question 14:
When is it not advisable to use the Wilcoxon test for independent samples?

When the data are normal and suit the t-test, which is more powerful.

When there are extreme values.

When the sample is small.

when the measurement is on an ordinal scale

Explanation:

When all the assumptions of the t-test hold, it is more powerful than Wilcoxon. Therefore Wilcoxon is less efficient in such cases.

Question 15

3.33 pts

Question 15:
The following diagram shows two groups and their ranks:

Which group has the higher values?

Group B

Group A

the two groups are equal

impossible to determine from ranks

Explanation:

Higher ranks → higher values. Group B shows higher ranks and therefore has higher values.

Question 16

3.33 pts

Question 16:
What is a common mistake in understanding the U statistic in the Mann Whitney test?

thinking it is a measure of the size of the gap, like a difference of means

Thinking it is a measure that depends only on the sample size.

Thinking it is always positive.

Thinking it must be smaller than 5.

Explanation:

U does not measure a gap between means but rather the degree of mixing between the two groups in the ranks.

Question 17

3.33 pts

17:
ranks A 40 B 80, because large more?

the two groups are completely identical

impossible to determine

Explanation:

ranks because . Yes B because more.

Question 18

3.33 pts

Question 18:
Why is Wilcoxon for independent samples suitable in situations with extreme values?

Because it ranks the values instead of working with them directly.

Because it deletes large values.

Because it normalizes the values.

Because it suits only normal distributions.

Explanation:

Ranking softens the impact of extreme values, so the test is more stable than the t-test.

Question 19

3.33 pts

Question 19:
What does a very small U relative to the sample size indicate?

The two groups barely overlap and are probably significantly different.

The groups are identical.

There is no difference between the groups.

The groups overlap completely.

Explanation:

A small U indicates that the ranks of one group are significantly lower than those of the other → a difference between the groups.

Question 20

3.33 pts

Question 20:
How do we explain in everyday language what the Wilcoxon test for independent samples does?

Tests whether the values of two groups are arranged one before the other when they are mixed and ranked.

Tests only the mean of each group.

Tests whether there is a relationship between the variables.

Tests whether the groups are dependent.

Explanation:

The test takes all the values from the two groups, mixes them, ranks them, and checks whether most of the high ranks come from one group → a sign of a real difference between the groups.

Question 21

3.33 pts

Question 21:
Below are two independent groups:

Group A	Group B
3	7
4	9
5	10

Which one likely has higher values?

Group B

Group A

Both are equal.

Cannot be determined.

Explanation:

All values of group B are higher than those of A, so it is clear that group B has higher values.

Question 22

3.33 pts

Question 22:
How are equal values handled when ranking in the Wilcoxon test for independent samples?

Assign all of them the average of the ranks.

Randomly draw a rank between the values.

Assign the lowest rank to all of them.

Assign the highest rank to all of them.

Explanation:

Equal values receive the average of the ranks they occupy. This is the standard treatment of ties.

Question 23

3.33 pts

Question 23:
Does Wilcoxon for independent samples require the distributions of the two groups to be similar?

No. It only requires independence and at least an ordinal measurement scale

Yes. The distributions must be identical

Yes. There must be symmetry

Yes. There must be normality

Explanation:

Wilcoxon does not assume identical or normal distribution. It only requires independence and a measurement scale that can be ranked.

Question 24

3.33 pts

Question 24:
If most of the high ranks were given to group A values, what does it mean?

Group A values are higher than group B.

Group B values are higher.

There is no relationship between ranks and values.

Nothing can be concluded.

Explanation:

High ranks indicate high values. If the high ranks appear in group A — group A values are higher.

Question 25

3.33 pts

Question 25:
In a small sample, if the ranks are almost equal between the groups, what is expected?

p is high — there is no evidence of a significant difference.

p is low — there is a significant difference.

Must use the t-test.

The result is invalid.

Explanation:

When the ranks are almost equal, there is no signal of a difference between the groups → p will be high and the null hypothesis is not rejected.

Question 26

3.33 pts

26:
because sample Wilcoxon independent?

larger samples increase power and the ability to detect a difference

larger samples reduce the power

sample size does not matter

only small samples work

Explanation:

: sample large more – more .

Question 27

3.33 pts

27:
Wilcoxon independent t-test independent?

Wilcoxon does not assume normality and is based on ranks

t-test does not test means

Wilcoxon requires equal variances

t-test is only suitable for a uniform distribution

Explanation:

Wilcoxon . t-test ( ).

Question 28

3.33 pts

28:
, A B No . :

A	B
88	72
90	75
92	70

more?

no way to determine

the two groups are identical

Explanation:

because A B, Yes A more. Wilcoxon ranks A.

Question 29

3.33 pts

29:
Wilcoxon independent?

whether/is "" because .

mean .

whether/is variables.

whether/is .

Explanation:

because ranks – ranks → more.

Question 30

3.33 pts

30:
Wilcoxon independent, p small?

There is a significant difference between the groups.

There is no difference between the groups.

The groups are identical.

The data are normal.

Explanation:

p small ranks → .