Parametric test of hypothesis testing

Statistical Testing in Research

1. Parametric and Non-Parametric Tests

Parametric Tests

Parametric tests are statistical tests that assume a specific distribution for the population (usually a normal distribution). These tests use parameters such as the mean and standard deviation to make inferences about the population.

Examples: t-test, ANOVA, z-test, Pearson correlation

Non-Parametric Tests

Non-parametric tests do not rely on any assumptions about the distribution of the population. These are used when data does not meet the assumptions of parametric tests, such as normality or equal variance.

Examples: Chi-square test, Mann-Whitney U test, Kruskal-Wallis test, Wilcoxon test

Comparison Table

2. t-Test

The t-test is a parametric test used to determine if there is a significant difference between the means of two groups. It is commonly used when sample sizes are small (n < 30).

Types of t-tests:

• One-sample t-test: Compares sample mean to known population mean.
• Independent two-sample t-test: Compares means from two independent groups.
• Paired sample t-test: Compares means from the same group at different times.

Example:

A teacher wants to know whether two teaching methods produce different results. The average scores of two groups of students are compared using a two-sample t-test.

3. Chi-Square (χ²) Test

The Chi-square test is a non-parametric test used to determine whether there is a significant association between two categorical variables. It compares the observed frequencies with expected frequencies.

Types of Chi-Square Tests:

• Chi-square test of independence: Tests if two variables are independent.
• Chi-square goodness-of-fit test: Tests how well an observed distribution fits an expected distribution.

Example:

A researcher wants to know if gender is related to preference for a new product. A chi-square test can be used to test the independence of gender and product preference.

Chi-Square Formula:

χ² = Σ (O - E)2 / E
Where O = Observed frequency, E = Expected frequency

Conditions for Applying Chi-Square Test:

• Data should be in frequency form.
• Observations must be independent.
• Expected frequency in each cell should be at least 5.

Limitations of Chi-Square Test:

• Cannot be used with small sample sizes.
• Not suitable for continuous data.
• Results may be misleading if assumptions are violated.