Difference between null hypothesis and alternative hypothesis.

The null hypothesis is a statement that there is no significant difference or relationship between two variables or groups in a study. It is typically the hypothesis that researchers aim to disprove or reject.

The alternative hypothesis, on the other hand, is a statement that there is a significant difference or relationship between the variables or groups being studied. It is the hypothesis that researchers are trying to provide evidence for or support.

In statistical hypothesis testing, researchers collect data and analyze it to determine whether the null hypothesis can be rejected in favor of the alternative hypothesis. If the data provides enough evidence to reject the null hypothesis, then the alternative hypothesis is accepted.

Null Hypothesis (H0)

- Statement that assumes no significant difference or effect
- Default hypothesis that is assumed to be true until proven otherwise
- Represented as "H0"
- Typically states that there is no difference (e.g., "H0: μ1 = μ2") or no effect (e.g., "H0: ρ = 0")

Alternative Hypothesis (Ha)

- Statement that contradicts the null hypothesis
- Proposes an alternative explanation or claim
- Represented as "Ha"
- States that there is a significant difference (e.g., "Ha: μ1 ≠ μ2") or effect (e.g., "Ha: ρ ≠ 0")

Key Differences:

- Directionality:
- Null hypothesis is non-directional (does not specify the direction of the difference or effect)
- Alternative hypothesis is directional (specifies that the difference or effect is in a particular direction)
- Burden of Proof:
- Null hypothesis is initially assumed to be true
- Alternative hypothesis must be supported by empirical evidence
- Statistical Significance:
- Statistical tests determine if the data provides sufficient evidence to reject the null hypothesis
- If the null hypothesis is rejected, the alternative hypothesis is supported