Non-parametric

Question 1

what do nonparametric statistical methods rely on instead of assuming a normal distribution?

Answer 1

they rely solely on the ranking of the subjects on the response variable

Question 2

in what scenarios are nonparametric methods especially useful?

Answer 2

1. when data are ranks rather than quantitative measurements
2. when assuming normality is inappropriate, such as with skewed distributions or small sample sizes

Question 3

what is the primary nonparametric method for comparing two groups?

Answer 3

the wilcoxon test

Question 4

what does the wilcoxon test compare?

Answer 4

it compares the ranks or mean ranks of two groups

Question 5

in the wilcoxon test, what does the null hypothesis typically state?

Answer 5

the treatments are identical in their effect on the response variable

Question 6

what is the alternative hypothesis in the context of the wilcoxon test?

Answer 6

that one treatment results in systematically better (or worse) rankings than the other

Question 7

how is the p-value calculated in the wilcoxon test?

Answer 7

by finding the probability of observing a test statistic as extreme or more extreme than the observed value, assuming H0 is true

Question 8

why is the wilcoxon test also called a “rank-sum test”?

Answer 8

because it can use the sum (or mean) of the ranks from one sample as the test statistic

Question 9

what happens when ties occur in rankings?

Answer 9

ties observations are assigned the average of their ranks

Question 10

how does the wilcoxon test handle quantitative data?

Answer 10

quantitative data are converted into ranks before performing the test?

Question 11

what assumption is required when estimating the difference between population medians using the wilcoxon test?

Answer 11

the population distributions of the two groups must have the same shape

Question 12

what does a sample proportion of 5/6 (as in the tanning experiment) indicate?

Answer 12

that the tanning studio was better in 5 out of 6 pairs of participants compared

Question 13

why might software like SPSS report a z statistic for large-sample wilcoxon tests?

Answer 13

because the sampling distribution of the test statistic approaches normality for large samples

Question 14

what does “no effect” correspond to in terms of sample proportions when comparing two groups?

Answer 14

a proportions of 1/2, indicating no systematic difference between groups

Question 15

why are nonparametric methods considered more robust than parametric methods?

Answer 15

they do not rely on strict assumptions about the underlying distribution of the data