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The t Test for Two Independent Samples - Coggle Diagram
The t Test for Two Independent Samples
Two-sample research designs: Studies that compare the mean scores of two sets of data, either from two separate groups of participants or from the same participants measured twice
Estimated standard error: The amount of error expected between a sample statistic and the population parameter. For a single-sample t test, it estimates how much sample means vary from the population mean.
Estimated standard error of the difference between means: Measures how much difference is expected between the sample mean difference and the true population mean difference.
Calculating the Estimated Standard Error: Using the sample variances and sample sizes from two independent groups to estimate how much the difference between their sample means is expected to vary by chance.
Independent-measures research design (between-subjects design): A research study that compares two separate groups of participants, with each group consisting of different individuals.
Repeated-measures research design (within-subjects design): A research study that uses the same participants to collect two or more sets of data, such as measuring their scores before and after a treatment.
Subscripts: Small numbers written beside a statistic to identify which sample it belongs to, such as (n_1) and (n_2) for sample sizes, (M_1) and (M_2) for sample means, and (SS_1) and (SS_2) for sums of squares.
Independent-measures hypothesis: The null hypothesis states that there is no difference between the two population means
Independent-measures t statistic: A test statistic used to compare the means of two separate, independent samples to determine whether there is a significant difference between them.
Pooled variance: A combined estimate of the population variance calculated by combining the variances from two independent samples.
Equal sample sizes: When two independent groups have the same number of participants or scores ((n1=n2)).
Assumptions of the independent-measures t test: The two samples must have independent observations, come from normally distributed populations, and have equal population variances (homogeneity of variance).
Estimated standard error: An estimate of how much difference is expected between a sample statistic and the population parameter due to chance.
Final formula and degrees of freedom: The independent-measures t test uses the difference between two sample means
Hypothesis tests with the independent-measures t statistic: A statistical test used to determine whether the difference between the means of two independent groups is significant or likely due to chance.
Directional hypotheses and one-tailed tests: A hypothesis test used when the researcher predicts the specific direction of a difference between two independent group means, such as one group scoring higher or lower than the other.
Hartley’s F-Max test: A statistical test used to determine whether two or more populations have equal variances by comparing the largest sample variance to the smallest sample variance.
Confidence intervals and hypothesis tests: Confidence intervals estimate the range where the true population difference is likely to fall, while hypothesis tests determine whether the difference between groups is statistically significant.
Cohen’s estimated d: A measure of effect size that shows how large the difference is between two sample means in relation to their pooled standard deviation.
Explained variance ((r^2)): The proportion of variability in the scores that can be explained by the difference between the two treatment conditions, expressed as a value between 0 and 1.
Error and the Role of Individual Differences: Error is the natural variation in scores that can affect research results, while individual differences are the unique characteristics of each person that can influence scores and make it harder to detect a treatment effect.