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📌In hypothesis testing, Type I and Type II errors refer to incorrect conclusions about the null hypothesis.

📌Type I Error (False Positive)

📍Occurs when we reject a true null hypothesis.

📍It means detecting an effect or difference when none actually exists.

📍Probability of making this error is denoted by α (significance level).

📌Type II Error (False Negative)

📍Occurs when we fail to reject a false null hypothesis.

📍It means missing a real effect or difference.

The t-test is a statistical test used to compare the means of two groups to determine if there is a significant difference between them.

📌Three Main Types of t-tests

1. Independent (Unpaired) t-test

📍Compares the means of two separate groups.

Example: Comparing test scores between male and female students.

2. Paired t-test (Dependent t-test)

📍Compares the means of the same group at two different times or conditions.

Example: Comparing students’ pre-test and post-test scores.

3. One-sample t-test

📍Compares the mean of a single sample to a known population mean.

📍Example: Testing if the average height of students in a school differs from the national average.

📌Each t-test assumes a normal distribution of the data and equal variance in independent t-tests unless adjustments (e.g., Welch’s t-test) are made.

📌QUANTITATIVE DATA ANALYSIS METHODS