Hypothesis Testing

Hypothesis: Framing Null Hypothesis and Alternative Hypothesis

Hypothesis

A hypothesis is a testable statement about the relationship between variables or an explanation for an observed phenomenon. It predicts the study’s findings and is either supported or not by the experiment’s outcome. Hypothesis testing is crucial to the scientific method.

Types of Hypotheses:

• Alternative Hypothesis (H1): The researcher’s prediction of a difference or effect.
• Null Hypothesis (H0): The prediction that there is no difference or effect, essentially the opposite of the alternative hypothesis.

Framing Null Hypothesis

The null hypothesis is a default statement that there is no relationship between two measured phenomena or no association among groups. Testing the null hypothesis involves determining if there is enough evidence to reject it, thereby suggesting a relationship exists.

Key Points:

• Null hypothesis is usually a statement of no effect or no difference.
• It is a precise statement about a population tested with sample data.
• The aim is to refute the null hypothesis to support the alternative hypothesis.

Examples:

• The correlation between frustration and aggression is zero.
• The average income for men is similar to that for women.
• Nationality is unrelated to music preference.
• The average population income was equal from 2012 to 2016.

Misconception:

• “Null” does not always mean zero. For example, a null hypothesis can state that the correlation between frustration and aggression is 0.5.

Limitations:

• Null hypothesis testing only indicates whether a population correlation is probably not zero, but it doesn’t tell the actual population correlation.

Framing Alternative Hypothesis

Alternative hypothesis is the statement that there is a statistical significance between two variables. It represents the outcome that the researcher is trying to prove.

Key Points:

• Indicates a difference or effect between variables.
• Empirical evidence is needed to refute the null hypothesis and support the alternative hypothesis.
• Denoted as H1.

Types:

• Directional Alternative Hypothesis: Predicts the direction of the effect (e.g., an increase or decrease).
• Non-Directional Alternative Hypothesis: Predicts an effect but does not specify the direction.

Example:

• In the Mentos and Diet Coke experiment, the alternative hypothesis is that Diet Coke will explode if Mentos is added.

Key Differences between Null and Alternative Hypothesis

• Relationship:
  • Null: No relationship between variables.
  • Alternative: There is a relationship or effect.
• Research Aim:
  • Null: The researcher tries to disprove it.
  • Alternative: The researcher tries to prove it.
• Observed Effect:
  • Null: No observed effect.
  • Alternative: Some observed effect.
• Actions:
  • Null accepted: No changes in opinions/actions.
  • Alternative accepted: Changes in opinions/actions.
• Parameters:
  • Null: Refers to population parameter (indirect testing).
  • Alternative: Refers to sample statistic (direct testing).
• Notation:
  • Null: H0.
  • Alternative: H1.
• Mathematical Formulation:
  • Null: Equal sign (e.g., =).
  • Alternative: Not equal sign (e.g., ≠).
• Outcome Source:
  • Null: Observations are due to chance.
  • Alternative: Observations are due to a real effect.

Conclusion

In hypothesis testing, the null hypothesis is either rejected in favor of the alternative hypothesis, or it is accepted. A null hypothesis represents no effect or difference, while an alternative hypothesis suggests a significant effect or difference.