Compare the following five types of tests Test Requirements

Compare the following five types of tests:

Test

Requirements

Types of data

1) What the test is used for

2) Example from business / economics

3) What for the test was used for in this example

Chi-square test

Independent t-test

Paired t-test

ANOVA

Wilcoxon rank-sum test

Test	Requirements	Types of data	1) What the test is used for 2) Example from business / economics 3) What for the test was used for in this example
Chi-square test
Independent t-test
Paired t-test
ANOVA
Wilcoxon rank-sum test

Solution

Test

Requirements

Types of data

1) What the test is used for

2) Example from business / economics

3) What for the test was used for in this example

Chi-square test

1. Quantitative data.

2. One or more categories.

3. Independent observations.

4.Adequate sample size (at least 10).

5. Simple random sample.

6. Data in frequency form.

7. All observations must be used.

Categorical

When we want to test whether one variable is independent of other or sample follows a particular distribution.

Independent t-test

1- Two samples must be independent.

2. Population standard deviations are unknown

3. There should be no significant outliers.

Numerical

when we want to compare two population means.

Paired t-test

1- Samples must be dependent.

2. The difference should be normally distributed.

Numerical

when we want to test before/after or in other words, same sample is analyzed in two conditions to see the effect.

ANOVA

1-There must be atleast 3 samples.

2-Samples must be independent.

3-There needs to be homogeneity of variances.

4-variables should be approximately normally distributed

Numerical

when we want to compare three or more population means.

Wilcoxon rank-sum test

1. When the requirements for the t-test for two independent samples are not satisfied, the Wilcoxon Rank-Sum non-parametric test can often be used provided the two independent samples are drawn from populations with an ordinal distribution.

Numerical

when we want to compare two population medians.

Test	Requirements	Types of data	1) What the test is used for 2) Example from business / economics 3) What for the test was used for in this example
Chi-square test	1. Quantitative data. 2. One or more categories. 3. Independent observations. 4.Adequate sample size (at least 10). 5. Simple random sample. 6. Data in frequency form. 7. All observations must be used.	Categorical	When we want to test whether one variable is independent of other or sample follows a particular distribution.
Independent t-test	1- Two samples must be independent. 2. Population standard deviations are unknown 3. There should be no significant outliers.	Numerical	when we want to compare two population means.
Paired t-test	1- Samples must be dependent. 2. The difference should be normally distributed.	Numerical	when we want to test before/after or in other words, same sample is analyzed in two conditions to see the effect.
ANOVA	1-There must be atleast 3 samples. 2-Samples must be independent. 3-There needs to be homogeneity of variances. 4-variables should be approximately normally distributed	Numerical	when we want to compare three or more population means.
Wilcoxon rank-sum test	1. When the requirements for the t-test for two independent samples are not satisfied, the Wilcoxon Rank-Sum non-parametric test can often be used provided the two independent samples are drawn from populations with an ordinal distribution.	Numerical	when we want to compare two population medians.