Inferential Statistics
- Inferential Statistics – Definition, Types, Examples, Formulas
- Observational Studies and Experiments
- Sample and Population
- Sampling Bias
- Sampling Methods
- Research Study Design
- Population Distribution, Sample Distribution and Sampling Distribution
- Central Limit Theorem
- Point Estimates
- Confidence Intervals
- Introduction to Bootstrapping
- Bootstrap Confidence Interval
- Paired Samples
- Impact of Sample Size on Confidence Intervals
- Introduction to Hypothesis Testing
- Writing Hypotheses
- Hypotheses Test Examples
- Randomization Procedures
- p-values
- Type I and Type II Errors
- P-value Significance Level
- Issues with Multiple Testing
- Confidence Intervals and Hypothesis Testing
- Inference for One Sample
- Inference for Two Samples
- One-Way ANOVA
- Two-Way ANOVA
- Chi-Square Tests
Independent and Paired Samples
Independent and Paired Samples
Independent and paired samples are two types of statistical comparisons that are commonly used in research studies. In both observational and experimental studies, we often want to compare two or more groups. When comparing two or more groups, cases may be independent or paired.
- Independent Groups
- Cases in each group are unrelated to one another.
- For example, in a study comparing the effectiveness of two different drugs, one group would receive Drug A and the other group would receive Drug B. The two groups are independent because the data for one group does not depend on the data for the other group.
- Paired Groups
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Cases in each group are meaningfully matched with one another; also known as dependent samples or matched pairs
For example, in a study comparing the effectiveness of a new therapy to an old therapy, the same group of patients would receive both treatments. The two groups are paired because the data for each patient in one group is related to the data for that same patient in the other group.
Independent samples Example
Suppose you want to compare the effectiveness of two different weight loss programs, Program A and Program B. You randomly select 50 participants and assign 25 of them to Program A and 25 to Program B. After 12 weeks, you measure the weight loss for each participant. Since the participants in Program A and Program B are randomly assigned and do not interact with each other, this is an example of independent samples.
Paired samples Example
Suppose you want to investigate the effect of a new medication on blood pressure. You select 30 patients with hypertension and measure their blood pressure before and after taking the medication for 4 weeks. Each patient serves as their control, and their blood pressure before taking the medication is paired with their blood pressure after taking the medication. This is an example of paired samples because the two sets of measurements are related to each other and are taken from the same group of patients.
Example: Shoes
A shoe company is studying how many shoes Italian men and women own. In one research study they take a random sample of 500 Italian adults and ask each individual if they identify as a man or women and how many pairs of shoes they own. The men and women in this study are in two independent groups.
In a second study the researchers use a different design. This time they take a random sample of 250 heterosexual married couples in Italy (i.e., 250 husbands and 250 wives). They record the number of shoes owned by each husband and each wife. This is an example of a matched pairs design. Data are paired by couple.