7.5.2.1 Probability and Significance

• What does probability measure in inferential statistics?

  Likelihood of outcome by chance
• In inferential statistics, probability is typically represented by the p-value
• What does a low p-value suggest in hypothesis testing?

  Unlikely due to chance
• A p-value of 0.05 means there is a 5% chance the results occurred by random chance if the null hypothesis is true.
• A study with a p-value of 0.02 indicates there is a 2% chance the results occurred by random chance
• What is the significance level (alpha) used for in statistical testing?

  Threshold for rejecting null hypothesis
• If the p-value is less than alpha (0.05), we reject the null hypothesis.
• A common value for alpha is 0.05
• What decision do we make if alpha = 0.05 and p-value =0.03?

  Reject null hypothesis
• Steps in the hypothesis testing process

  1️⃣ State the Null Hypothesis

  2️⃣ State the Alternative Hypothesis

  3️⃣ Choose the Significance Level

  4️⃣ Perform the Statistical Test

  5️⃣ Make a Decision
• Match the step in hypothesis testing with its description:

  Null Hypothesis ↔️ No significant difference

  Alternative Hypothesis ↔️ Significant difference exists

  Significance Level ↔️ Threshold for rejection

  P-value ↔️ Likelihood of chance results
• What statistical test was used in the example provided?

  Independent t-test
• If the p-value is typically less than 0.05, it suggests the results are unlikely due to chance
• What does a p-value of 0.02 indicate in hypothesis testing?

  2% chance of random results
• If the p-value is greater than alpha, we reject the null hypothesis.

  False
• What conclusion can be drawn if alpha = 0.05 and the p-value = 0.03?

  Reject the null hypothesis
• What do you conclude if the p-value is 0.03 and α = 0.05?

  Reject the null hypothesis
• The significance level (alpha, α) is a threshold used to determine whether results are unlikely to have occurred by chance
• A common value for α is 0.05.
• What should you do if the p-value is less than α?

  Reject the null hypothesis
• What does the Null Hypothesis assume?

  No significant difference
• The typical value for the significance level α is 0.05
• If p < α, you reject the null hypothesis.
• What should you do if p ≥ α?

  Fail to reject the null hypothesis
• Medication A and B have no effect on blood pressure is an example of a null hypothesis.
• Match the statistical test with its purpose and data type:

  t-test ↔️ Compares means of two groups with continuous data

  Chi-squared test ↔️ Tests associations between two categorical variables