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The t Test for Two Independent Samples - Coggle Diagram
The t Test for Two Independent Samples
Tools you need to know
Sample variance (Chapter 4)
Standard error formulas (Chapter 7)
The t statistic (Chapter 9)
Distribution of t values
df for the t statistic
Estimated standard error
independent-measures research design
A research design that uses a separate group of participants for each treatment condition (or for each population) is called an independent-measures research design or a between-subjects design.
pooled variance
One method for correcting the bias in the standard error is to combine the two sample variances into a single value
Directional Hypotheses and One-Tailed Tests
State the Hypotheses and Select the Alpha Level
Locate the Critical Region
Collect the Data and Calculate the Test Statistic
Make a Decision
There are three assumptions that should be satisfied before you use the independent-measures t formula for hypothesis testing:
The observations within each sample must be independent (see page 264).
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.
homogeneity of variance
states that the two populations being compared must have the same variance.
most important when there is a large discrepancy between the sample sizes.
Violating the homogeneity of variance assumption can negate any meaningful interpretation of the data from an independent-measures experiment.
The F-max test is based on the principle that a sample variance provides an unbiased estimate of the population variance.
Compute the sample variance, , for each of the separate samples.
Select the largest and the smallest of these sample variances and compute
Cohen’s Estimated d
You should note that standard deviation is not a step in the computations for the independent-measures t test
yet it is useful when providing descriptive statistics for each treatment group.
It is easily computed when doing the t test because you need SS and df for both groups to determine the pooled variance
Key Terms
independent-measures research design or between-subjects design
repeated-measures research design or within-subjects design
independent-measures t statistic
estimated standard error of
pooled variance
homogeneity of variance
estimation can be used to get an indication of the significance of the effect.
You should recognize that a mean difference of zero is exactly what would be predicted by the null hypothesis if we were doing a hypothesis test
outcome of a hypothesis test is influenced by a variety of factors,
including the size of the sample(s) used in the research study
