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The t Test for Two Independent Samples - Coggle Diagram
The t Test for Two Independent Samples
Intro to the Independent-Measures Design
Independent-Measure Research Design
A research design that uses a separate group of participants for each treatment condition (or for each population)
two sets of data could come from two completely separate groups of participates
two sets of data could come from the same group of participants
Hypotheses and the Independent-Measures t Statistic
Hypotheses for an Independent-Measures Test
H0= u1-u2=0 (no difference between the population means)
H1= u1-u2=/ 0 (there is a mean difference)
Overall t Formula
single sample t = sample mean-population mean/estimated standard error
independent-measures t= sample mean difference-population mean difference/estimated standard error of sample mean difference
Calculating the Estimated Standard Error
Pooled Variance
Estimated Standard Error
Final Formula and Degrees of Freedom
Hypothesis Tests w/ the Independent-Measures of t Statistic
Directional Hypotheses and One-Tailed Tests
When planning an independent-measures study a researcher usually has some expectation or prediction of the outcome
One-tailed tests should be used when clearly justified by theory or previous findings
State the hypothesis and selected the alpha level
Locate the critical region
Collect the data and calculate the test statistic
Make a decision
Assumptions Underlying the Independent-Measures t Formula
The observations within each sample must be independent
The two populations from which the samples are selected must be normal
The two populations from which the samples are selected must have equal variances
Effect Size and Confidence Intervals
The Role of the Sample Variance and Sample Size in the Independent Measures t Test
only variance has a large influence on measures of effect size such as Cohen's d and r^2
