Hypothesis Testing 02: 10 Steps

Hypothesis Definition

  • A hypothesis is a statement about a particular population.

  • It involves making predictions about measurable aspects such as average height or response to a medication.

  • Hypotheses serve as educated guesses about population parameters that cannot be known with certainty.

Types of Hypotheses

Research Hypothesis

  • The research hypothesis drives the research and is often based on experience or previous studies.

  • Example: "Patients' blood pressure will drop as a result of this medication."

Statistical Hypothesis

  • The statistical hypothesis is structured for statistical testing.

  • Example: "In men aged 40 to 60 years, the mean drop in blood pressure with the medication will be 10 mmHg."

Steps of Hypothesis Testing

Step 1: Data Collection

  • Collect data from a sample population, involving measurements or counts (e.g., blood pressure, event outcomes).

Step 2: Make Assumptions

  • Assess data distribution: check if it is normally distributed.

  • Determine known values, such as standard deviation, to choose between Z or T scores in later steps.

Step 3: State the Hypotheses

Null Hypothesis (H0)

  • Represented by H0, it typically states that there is no difference or effect (e.g., "The mean is equal to 50.").

Alternative Hypothesis (H1 or Ha)

  • Represents what the researcher aims to prove (e.g., "The mean is not equal to 50.").

  • The hypotheses must complement each other:

    • Ha: mean > 50; H0: mean ≤ 50

    • Ha: mean < 50; H0: mean ≥ 50

Step 4: Choose a Test Statistic

  • Select the test statistic (Z-score or T-score) based on known or unknown standard deviations:

    • Z-score: used when population standard deviation is known.

    • T-score: used when population standard deviation is unknown, utilizing sample standard deviation instead.

Step 5: Determine Distribution of Test Statistic

  • Identify if using a Z or T distribution based on previous assessments.

Step 6: Establish the Decision Rule

  • Set a significance level (Alpha), typically 0.05 (5%).

  • Alpha indicates the probability of rejecting a true null hypothesis:

    • 5% chance corresponds to a two-tailed test (accepting the null hypothesis if test statistic falls within 95% area).

Step 7: Calculate the Test Statistic

  • Use formula:

    • Test Statistic = (Sample Mean - Hypothesized Mean) / Standard Error

  • Standard Error is based on known or estimated statistics.

Step 8: Make a Statistical Decision

  • Determine if the test statistic falls within the acceptance or rejection regions:

    • Reject H0 if falls in the rejection areas; accept if falls in acceptance areas.

Step 9: Conclusion

  • If H0 is rejected, there is evidence to support Ha; otherwise, may accept H0 as true.

Step 10: Calculate the P-value

  • The P-value represents the probability of obtaining the observed test statistic.

  • It helps determine how likely the findings are under the null hypothesis (e.g., a P-value of 0.05 indicates 5% likelihood).

Summary of Hypothesis Testing Steps

  • The process is systematic and consists of straightforward steps, crucial for drawing valid statistical conclusions.