Statistical Methods for Mean Differences in Health Sciences

스터디 가이드 - 스마트 노트

자료에 맞춘 맞춤형 노트, 핵심 정의, 예시, 맥락을 확장해 제공합니다.

Applied Statistics for the Health Sciences

Course 3: Differences between groups and conditions

This section introduces statistical methods for comparing mean differences between groups or conditions, with a focus on parametric and non-parametric tests, independent and repeated measures, and practical applications in health sciences.

Overview of Statistical Comparisons

Main Types of Mean Difference Tests

Mean differences between two groups or conditions: Assessing whether the average values differ significantly between groups.
Parametric and non-parametric tests: Selection depends on data distribution and sample characteristics.
t-test for independent samples: Used when comparing two separate groups.
t-test for repeated measures (paired samples): Used when the same subjects are measured under different conditions.

Review of Hypothesis Testing

Research Questions and Hypotheses

Null Hypothesis (H0): Assumes no difference or effect between groups or conditions.
Alternative Hypothesis (H1): Assumes a significant difference or effect exists.
Statistical Significance: Determined by p-values; a result is considered significant if p < 0.05.

Example: Testing whether a new drug improves patient outcomes compared to a placebo.

Mean Difference Between Two Groups or Conditions

Purpose and Application

Assessing Mean Scores: Researchers may compare the mean scores of two samples to determine statistical significance.
Example Application: Comparing the benefits of intensive rehabilitation in patients with chronic obstructive pulmonary disease (COPD) versus standard care.

Parametric and Non-Parametric Tests

Types of Statistical Tests

Parametric Tests: Assume data are normally distributed and have equal variances. Common examples include the t-test and ANOVA.
Non-Parametric Tests: Used when data do not meet parametric assumptions. Examples include the Mann-Whitney U test and Wilcoxon signed-rank test.

Key Point: Parametric tests are more powerful when assumptions are met, but non-parametric tests are more robust to violations of normality and homogeneity of variance.

t-Test for Independent Groups

Definition and Application

Independent Samples: Two groups are unrelated (e.g., treatment vs. control).
Research Example: Comparing the effectiveness of a new drug in multiple sclerosis patients versus a control group.

Hypotheses:

Null hypothesis:
Alternative hypothesis:

Steps to Verify t-Test Results with SPSS

Verify the result of the Levene's test for equality of variances.
If p < 0.05, use the row for unequal variances; otherwise, use the row for equal variances.
Check the p-value of the t-test. If p < 0.05, the difference between means is significant.
If significant, examine the means of the two groups to identify the direction of the difference.
Calculate the effect size (small, medium, large).

Effect Size Calculation

Cohen's d: Measures the standardized difference between two means.

Small effect: d = 0.2
Medium effect: d = 0.5
Large effect: d = 0.8

t-Test for Repeated Measures (Paired Samples)

Definition and Application

Repeated Measures: The same subjects are measured under two conditions (e.g., before and after treatment).
Research Example: Determining whether patients with multiple sclerosis score lower on a verbal IQ task than on a performance IQ task.

Hypotheses:

Null hypothesis:
Alternative hypothesis:

Steps to Verify t-Test Results with SPSS

Verify the result of the t-test.
If p < 0.05, the difference between means is significant.
If significant, examine the means to identify the direction of the difference.
Calculate the effect size (small, medium, large).

Summary Table: Parametric vs. Non-Parametric Tests

Test Type	Assumptions	Common Tests	When to Use
Parametric	Normal distribution, equal variances	t-test, ANOVA	Data meets assumptions
Non-Parametric	No assumption of normality	Mann-Whitney U, Wilcoxon signed-rank	Data does not meet parametric assumptions

Interpretation of Results

Key Points

Statistical Significance: Indicates whether observed differences are likely due to chance.
Effect Size: Quantifies the magnitude of the difference.
Direction of Difference: Determined by comparing group means.

Additional info:

SPSS is a statistical software commonly used for performing t-tests and other analyses in health sciences.
Effect size is important for understanding practical significance, not just statistical significance.