Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions or inferences about a population based on experimental(sample) data. Hypothesis Testing is basically an assumption that we make about the population parameter.

Types of hypothesis testing in statistics:

• Based on the Number of Samples and Tails:
  • One-Sample Hypothesis Testing: Compares a single sample to a hypothesized value (mean, proportion, etc.).
  • Two-Sample Hypothesis Testing: Compares two independent samples to assess if there's a significant difference between them.
  • Paired-Sample Hypothesis Testing: Compares data from the same group or individuals measured at different times or under different conditions.
• Based on the Direction of the Alternative Hypothesis:
  • Two-Tailed Hypothesis Testing: Seeks evidence to reject the null hypothesis in either direction (greater than or less than the hypothesized value). Used when the direction of the effect is unknown.
  • One-Tailed Hypothesis Testing: Seeks evidence to reject the null hypothesis in a specific direction (greater than or less than the hypothesized value). Used when you have a strong prior Expectation about the direction of the effect.
• Based on the Type of Data:
  • Parametric Hypothesis Testing: Assumes the data follows a specific probability distribution (e.g., normal distribution) and utilizes tests like t-tests, z-tests, and ANOVAs.
  • Non-parametric Hypothesis Testing: Doesn't rely on specific assumptions about the underlying data distribution and uses tests like Wilcoxon signed-rank test, Mann-Whitney U test, and Chi-Square Test.
• Additional types of hypothesis testing encountered in specific contexts:
  • Chi-Square Test for Independence: Assesses if two categorical variables are statistically related.
  • Chi-Square Goodness-of-Fit Test: Compares the observed distribution of a categorical variable to an expected distribution.
  • Correlation Analysis: Measures the strength and direction of a Linear Relationship between two continuous variables.
  • Regression Analysis (Regression): Explores the relationship between a dependent variable and one or more independent variables.

Steps:

1. Formulate Hypotheses
   • Null Hypothesis: Assuming the effect is insignificant.
   • Alternate Hypothesis: Assuming the effect is significant.
2. Choose Significance Level ()
3. Collect Data
4. Conduct Statistical Test: E.g. T-test, Chi-Square Test, ANOVA, …
5. Decision Rule
   • If the p-value is less than or equal to the significance level (), reject the null hypothesis.
   • If the p-value is greater than the significance level, do not reject the null hypothesis.
6. Draw a Conclusion: Accept or reject null hypothesis.
7. Make Interpretations
   • Type I error: It is a false positive conclusion about hypothesis, where it is rejected when it is, in fact, true.
   • Type II error: It is a false negative conclusion about hypothesis, where it is not rejected when it is, in fact, false.