Statistics: Hypothesis and Errors Quiz

Comparing Means of Two Samples

• When comparing the means of two samples from one population, it is expected that the two samples are representative of the population and that there is no significant difference between their means.

Two Independent Samples T-Test

• Condition NOT required: Equal variances between the two samples. Levene's Test is used to assess this assumption.

Levene's Test

• P > 0.05: Implies that there is no significant difference in variances between the two groups, meaning the assumption of equal variances is met.

Probability of Type I and II Errors

• Conditions that increase the probability of Type I and II errors:
  • Small sample sizes
  • Large variability within groups
  • Significant differences in group means

Two Independent Samples T-Test Research Question

• Example research question: Does a new medication reduce blood pressure compared to a placebo control group?

Alternative Hypothesis (H_a)

• Indicates the expected relationship between the variables being tested, suggesting a difference or effect.

Type I Error

• Rejecting the null hypothesis when it is actually true.

Significance Level (α)

• Commonly chosen value: 0.05, meaning there is a 5% chance of making a Type I error.

Purpose of Hypothesis Testing

• Determine if there is enough evidence to reject the null hypothesis and support the alternative hypothesis.

Power of Hypothesis Test

• The probability of correctly rejecting the null hypothesis when it is false.

P-value Greater than Significance Level (α)

• Indicates insufficient evidence to reject the null hypothesis.

Hypothesis Usually Rejected

• The null hypothesis is usually set up to be rejected.

Sampling Method when Population is Large

• Typically used method: Sampling, selecting a smaller representative group from the population to study.

Significance Level (α = 0.05)

• Indicates a 5% chance of rejecting a true null hypothesis (Type I error).

Condition for One-Sample T-Test

• Necessary condition: The data should be normally distributed.

Type I Error

• Occurs when: The null hypothesis is rejected, but it is actually true.

P-value

• The probability of observing the given data or more extreme data, assuming the null hypothesis is true.

Power of a Test

• The probability of correctly rejecting the null hypothesis when it is false.

Null Hypothesis

• True statement: The null hypothesis is assumed to be true until proven otherwise.

Alternative Hypothesis vs. Null Hypothesis

• Distinguishing feature: The alternative hypothesis states the opposite of the null hypothesis.

T-Test for Comparing Two Group Means

• Statistical test: Two-sample t-test.

Null Hypothesis (H₀) for Triglyceride Levels

• H₀: There is no difference in triglyceride levels between the two groups.

Observed T-value Greater than Tabular T-value

• Conclusion: The null hypothesis is rejected, indicating a significant difference between the group means.

Test Statistic for Triglyceride Levels

• Calculated test statistic: T-value.

P-value in Analysis

• The probability of observing the given data or more extreme data, assuming the null hypothesis is true.

P-value and Significance Level

• Conclusion based on p-value = 0.010 and α = 0.05: The p-value is less than the significance level, leading to the rejection of the null hypothesis.

Alternative Hypothesis (H1) for Triglyceride Levels

• H₁: There is a difference in triglyceride levels between the two groups.

Calculated T-Test Value

• The calculated T-value represents the difference between the two group means, scaled by the standard error of the difference.

Condition NOT Required for Two Independent Sample T-test

• Condition: Equal variances between the two samples. However, even if variances are not equal, the t-test can still be performed using modifications for unequal variances.

Test your knowledge on hypothesis testing, including the definitions of null and alternative hypotheses, and the concepts of type I and type II errors. This quiz covers the essential steps and procedures involved in hypothesis testing, P-values, and the power of a test. Perfect for students learning statistical significance!