Lecture 9 - Nonparametric Tests

Question 1

Define parametric statistics.

Answer 1

Statistical techniques based on assumptions about the population from which the sample data has been collected.

Question 2

What are some advantages of non-parametric statistics as compared to parametric statistics? (4 points)

Answer 2

1) They make fewer assumptions about the population.
2) They can be used for smaller sample sizes.
3) They can be used on categorical data (nominal or ordinal.
4) They can be computed by hand.

Question 3

What are some disadvantages of non-parametric statistics as compared to parametric statistics? (3 points)

Answer 3

1) Can be wasteful of data (not all info used)
2) Not as widely known
3) Calculations can be tedious.

Question 4

What does the Mann-Whitney U Test compare?

Answer 4

The means for two independent samples.

Question 5

What are the two assumptions of the Mann-Whitney U test?

Answer 5

1) Independent samples

2) At a minimum ordinal data

Question 6

What is the cut off for the small sample Mann-Whitney U test?

Answer 6

Both sample sizes must be less than 10.

Question 7

What are the 4 steps needed to conduct the Mann-Whitney test?

Answer 7

1) Rank the n observations, tied observations receive the average rank
2) Let the sum of the ranks from group 1 be W1 and sum for group 2 be W2
3) Determine the U stat using the formula sheet for each group
4) Use the smaller of the two values for the stat

Question 8

Which formula is for the Mann-Whitney large sample test?

Answer 8

The one with the z stat associated with it.

Question 9

What does the Kruskall-Wallis Test evaluate?

Answer 9

Whether c groups of known sizes are identical (i.e. come from the same population.

Question 10

What are the 2 assumptions of the Kruskall-Wallis Test?

Answer 10

1) That all c groups are independent

2) That individual items are randomly selected

Question 11

Does the Kruskall Wallis Test assume a population shape or non-ordinal data?

Answer 11

No, any pop shape and ordinal data are both fine

Question 12

What are the 5 steps for the Kruskall Wallis Test?

Answer 12

1) Pool and rank all observations
2) Give tied values the average of all tied ranks
3) Calculate Ti (sum of ranks for sample i) for all samples
4) Compute the K stat using the formula
5) Reject Ho if the test stat > Critical value (the chi square crit using df = c - 1)

Question 13

What does the Kolmogorov-Smirnov Test evaluate?

Answer 13

Whether the sample conforms to a normal distribution.

Question 14

What are the two advantages of the Kolmogorov-Smirnov Test over the chi square goodness of fit test?

Answer 14

1) It does not require the expected frequencies to be at least 5
2) It has a higher probability of rejecting a false null hypothesis

Question 15

What is the disadvantage of the Kolmogorov-Smirnov test compared to the chi square test?

Answer 15

The population parmaters (mean and std dev) must be known (not estimated from sample data)

Question 16

What two values are calculated for the Kolmogorov-Smirnov test and what letters are associated with each?

Answer 16

Fi - Observed cumulative relative frequency

Ei - Expected cumulative relative frequency

Question 17

What are the 4 steps in the Kolmogorov-Smirnov test?

Answer 17

1) Divide the range of random variables into c classes with upper boundaries X1, X2 … Xc
2) For each of the c classes calculate Fi and Ei
3) Calculate the test stat, D = the maximum of the absolute values of the difference between Fi and Ei
4) Reject the null hypothesis if D exceeds the crit value obtained from Kolmogorov-Smirnov tables

Question 18

How is the Lilliefors test different from the Kolmogorov-Smirnov test? (2 points)

Answer 18

1) It is used when the pop mean and std dev are unknown

2) Instead of using the Kolmogorov-Smirnov table to determine the test stat the lilliefors table is used