Hypothesis Testing Concept Overview

Hypothesis Testing Concept

• A statistical method used to determine if enough evidence exists in a sample to support a particular belief (hypothesis) about a population.
• Used in scientific research to make inferences and decisions based on sample data.

Importance of Hypothesis Testing

• Helps in making data-driven decisions.
• Essential for validating research findings and determining the effectiveness of drugs, treatments, and other interventions.

Steps in Hypothesis Testing

• State the Hypotheses

  • Null Hypothesis (H0): A statement that there is no effect or no difference. Serves as the default or starting assumption.
    • Example: "The new drug has no effect on blood pressure."
  • Alternative Hypothesis (Ha): A statement that there is an effect or a difference. What you want to prove.
    • Example: "The new drug lowers blood pressure."

• Choose the Significance Level (α)

  • The probability of rejecting the null hypothesis when it is true.
  • Common values are 0.05 (5%) or 0.01 (1%).

• Collect and Summarize the Data

  • Obtain a sample and calculate relevant statistics such as mean, standard deviation, or proportion.

• Calculate the Test Statistic

  • Based on the data, calculate a value that helps determine whether to reject or not reject the null hypothesis.

• Determine the p-value

  • The probability of obtaining the observed results if the null hypothesis is true..
  • A smaller p-value suggests stronger evidence against the null hypothesis.

• Make a Decision

  • If the p-value is less than the significance level (α), reject the null hypothesis.
  • If the p-value is greater than the significance level (α), do not reject the null hypothesis.

Types of Hypotheses

• Null Hypothesis (H0): Represents the status quo or no change.

  • Example: "The average cholesterol level of patients taking drug X is equal to 200 mg/dL."

• Alternative Hypothesis (Ha): Represents a new claim or change.

  • Example: "The average cholesterol level of patients taking drug X is different from 200 mg/dL."

Understanding p-value and Significance Level (α)

• p-value:
  • The probability of obtaining a result equal to or more extreme than what was actually observed, under the assumption of no effect or no difference (null hypothesis).
• Significance Level (α):
  • The threshold set for rejecting the null hypothesis, often set at 0.05 (5%).

Decision Rule:

• If p-value ≤ α: Reject H0.
• If p-value > α: Do not reject H0.

Example

• A new drug is tested to see if it reduces blood pressure more effectively than a placebo.
• Null Hypothesis (H0​): The new drug has no effect on blood pressure (it is the same as the placebo).
• Alternative Hypothesis (Ha​): The new drug reduces blood pressure more than the placebo.

Errors in Hypothesis Testing

• Type I Error (α):

  • Rejecting H0 when it is true (false positive).
  • Example: Concluding a drug is effective when it is not.

• Type II Error (β):

  • Not rejecting H0 when it is false (false negative).
  • Example: Concluding a drug is not effective when it actually is.