Nonparametric tests

Question 1

Which statistic is used to perform the median test?

Answer 1

The Chi-square statistic

Question 2

What is the formula of the Chi-square variate?

Answer 2

summation of the ratio of square of difference between (obs freq to the expected freq) to the expected frequency for each observation.

Question 3

What is the null hypothesis of one sample median test?

Answer 3

The median of the population distribution is Mdo.

Question 4

How is the test statistic calculated in the one sample median test?

Answer 4

1. A is assigned for obs less that Mdo and B is assigned for the obs more that Mdo and O is assigned for the obs equal to Mdo.
2. Number of expected frequency is calculated for each A and B eliminating O. The formula for expected frequency is half of effective sample size.
3. With the obs and expected frequency obtained, the chi-square statistic is calculated.

Question 5

What is the null hypothesis for the two-sample median test?

Answer 5

The medians are equal. This can mean following things:
1. The samples are drawn from the same population or two different populations having same distribution function.

Question 6

What is the test statistic of two sample median test?

Answer 6

a = No. of obs. less than or equal to the sample median.
The sample median is calculated by combining the two samples. Remember that two samples have to be arranged in ascending order to calculate median.

Question 7

How is test statistic calculated for the two-sample median test?

Answer 7

1. Combine the two samples and arrange them in ascending order.
2. Calculate the median of the combined sample.
3. Find the no. of obs. less or equal to the median in first sample.

Question 8

Why do not we calculate the expected frequency in the two-sample median test?

Answer 8

I don’t know the answer, but one thing is our test statistic follows the hypergeometric distribution.

Question 9

What is done with the test statistic in the two-sample median test?

Answer 9

p-value is calculated for the probability of the test statistic to be higher than the obs.

Question 10

How is decision taken for the two-sample median test?

Answer 10

After calculating the p-value, the process of taking decision is same as in other test where p-value is involved.

Question 11

How is the p-value related to the decision of the test? What is the philosophy behind the analysis of p-value?

Answer 11

I don’t know exactly what is behind this. Search.

Question 12

Why is p-value is always taken as the probability of test statistic being higher than obtained? Why not lower?

Answer 12

This is not the case. In binomial test, the p-value is taken as the probability of binomial variable being less than the test statistic.

Question 13

What factor in a non-parametric affects the following:
whether p-value is taken as the probability of the variable being more than the test statistic, or less?

Answer 13

I don’t know the answer. But I have to figure out the meaning of the test statistic and its distribution in each test.

SEARCH THE ANSWER OF THIS.

Question 14

In which median test, the test statistic is not the Chi-square variate?

Answer 14

Two-sample median test. But why though? How is different principle involved in this?

Question 15

Why is Chi-square statistic being employed in the median test?

Answer 15

because Chi-square test is used to test the identicalness of the k sample on the basis of the frequencies of the samples. Hence, that theory is being applied in the median test.

Question 16

What is the null hypothesis of k-samples median test?

Answer 16

All samples have been drawn from the identical population with the same median.

Question 17

What is the test statistic for the k-sample median test?

Answer 17

The summation of the ratio of square of the difference between observed and the expected frequency to the expected frequency.

Question 18

How is expected frequency of the individual obs. calculated in the k sample median test?

Answer 18

The formula for expected frequency of each obs. is given by the ratio of the product of Row total and Column total to the grand total.

Question 19

How is the test statistic calculated in the k-sample median test?

Answer 19

1. Combine all the samples and calculate the median.
2. List the samples in a column. And list the corresponding no of obs. less (or equal) than median and more than median row-wise for each sample.
3. Add a row for column total and a column for row total.

Question 20

How do you calculate Chi- square once you obtained the expected frequencies?

Answer 20

Draw a table and for each obs. freq. the expected freq. is recorded, and the required ration is calculated from the table.

Question 21

When is Cochran Q test is used?

Answer 21

To test whether three or more matched set of frequencies or proportions differ significantly among themselves or not.
Remember, the similarities between samples are best recognized by Chi-square test.

Question 22

In which test, the dichotomized observations are used?

Answer 22

The Cochran Q test.

Question 23

What is the test statistic for the Cochran Q test?

Answer 23

There is a formula for Q. Look at the notes.

Question 24

What does the contingency table of Cochran Q test look like?

Answer 24

1. Treatments or samples are taken in a column, and the no. of objects given that treatment is recorded in successive columns.
2. The success and failure of each test for each object are recorded.
3. Row total and column total are made for the total successes in a row and a column respectively.
4. Then n = total no. of success for all objects for all the treatments
5. From then, the test statistic can be found.

Question 25

Which distribution does the test statistic of Cochran Q test follow?

Answer 25

Chi-square variation

Question 26

What kind of random samples’ statistic follow Chi-square distribution?

Answer 26

I don’t know. Investigate how do a statistician know a particular statistic follows a particular distribution, particularly Chi-square.

Question 27

Why do we don’t have to calculate p-value when a chi-square is associated? And why do we have to calculate p-value? For what kinds of distributions?

Answer 27

–unfilled answer–

Question 28

What is one way classification or completely randomized design (CRD)?

Answer 28

–unfilled answer–

Question 29

Which test is also called one-way ANOVA test?

Answer 29

Kruskal Wallis H test

Question 30

When is Kruskal Wallis H test is used?

Answer 30

To test whether three or more samples differ significantly in location (median) or not.

Question 31

What does the observation table of Kruskal Wallis H test look like?

Answer 31

1. Samples are arranged in one column. And the frequencies of each sample are recorded in successive columns.
2. Total number of objects in each sample is recorded at the last column.

Question 32

What does the contingency table of Kruskal Wallis H test look like?

Answer 32

1. All samples are combined and ranked.
2. The rank of each obs. is placed at the same place, of the obs. table, where the obs. was recorded.
3. Total ranks are obtained at the last column of each row (each row is for a sample).

Question 33

What is the formula for the test statistic of Kruskal Wallis H test?

Answer 33

Refer note if you don’t know.

Question 34

Which distribution does the H statistic for Kruskal Wallis H test follow?

Answer 34

1. For small sample case, p-value is calculated. This is seen from the Kruskal Wallis H Table. (I don’t know the exact distribution).
2. In case of large sample case, the Kruskal Wallis H test statistic follows chi-square distribution with k-1 degrees of freedom.

Recall: The process of taking the decision should be clear from the above cases.

Question 35

What is the small sample case and large sample case for Kruskal Wallis H test?

Answer 35

For small sample: k is equal to 3 and each sample has 5 or less obs.

For large sample case, K is greater or equal to 3 and each sample has 5 or more obs.

Question 36

What is two-way classification and randomized block design?

Answer 36

–unfilled answer–

Question 37

For how many numbers of samples, is the Friedmann Two-Way ANOVA Test valid?

Answer 37

There should be more than two samples.

Question 38

What is the null hypothesis of Friedmann Two-Way ANOVA Test?

Answer 38

All samples have same median.

Question 39

How is Friedmann Two-Way ANOVA Test different from the median test if they both have the same null hypothesis?

Answer 39

–unfilled answer–

Question 40

What is the test statistic for the Friedmann Two-Way ANOVA Test?

Answer 40

Refer to the notes if you don’t know.

Question 41

How is contingency table prepared for the Friedmann Two-Way ANOVA Test?

Answer 41

1. First, the samples are obtained, and different blocks are written same as that of the question.
2. Now the frequencies are ranked column-wise (i.e. for each block the ranking is done separately column-wise).
3. The row total of ranking of each row is recorded at the last column, and for each sample i, the row total is denoted by Ri.
4. From these data, Friedmann Two-Way ANOVA statistic can be calculated.

Question 42

Write down the correction for both Friedmann Two-Way ANOVA Test and Krushkal Wallis H Test.

Answer 42

Refer to the notes if you don’t know the answer.

Question 43

In which case, the correction is applied for Friedmann Two-Way ANOVA Test and Krushkal Wallis H Test?

Answer 43

When the number of tied cases is significant.

Question 44

How is the decision made for the Friedmann Two-Way ANOVA Test?

Answer 44

1. For small sample case, the p-value (probability of H being more than the calculated value) is obtained.
2. For large sample case, the statistic follows chi-square distribution, and the decision is taken according to the chi-square test.

Question 45

What is the small sample case and large sample case for the Friedmann Two-Way ANOVA Test?

Answer 45

1. Small sample case: k is 3 and n lies between 2 and 9 including the boundaries. OR k is 4 and n lies between 2 and 4 including the boundaries.
2. Large sample case: k is greater than 3 and n is greater than 4. OR when wither k or n exceeds 5