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T-test Independent Samples, The following assumptions should be met before…
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The following assumptions should be met before using the independent-measures t formula for hypothesis testing:
1- observations within each sample must be independent
2-two populations from which the samples are selected must be normal
3-homogeneity of variance: two populations from which samples are selected must have equal variances.
independent observations:
1-there is no consistent, predictable relationship between between the first and second observations
2-two events are independent if the occurrence of the first event has no effect on the probability of the second event.
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1- compute the sample variance for each separate samples
2- select the largest and the smallest of the sample variances and compute. A large f-max indicates large difference between the sample variance and homogeneity has been violated. A small f-max value (near 1.00) indicates the sample variance is similar and homogeneity is reasonable.
3- f-max value computed is compared with the critical value for the f-max statistic.
Hartley's F-max test is a simple test that assesses the homogeneity assumption. F-max test is based on the principle that a sample variance provides an unbiased estimate of the population variance. This test states the null hypothesis population variance are equal; and sample variance should be similar.
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Cohen's d measuring effect size in the context of an independent-measures research:
r2 formula is the same for independent-measures t is exactly the same as it is for single-sample t
Confidence intervals calculation