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Why is t used instead of z?
t should be used instead of z when the population standard deviation (σ) is not known.
When is a single-sample t-test appropriate?
A single-sample t-test is appropriate when there is a single sample of subjects providing one score, and the research questions about the population value compared to a known value.
What distinguishes the t distribution from the z distribution?
The t distribution is based on many distributions and has more variability than the normal distribution used for z, which is why critical values for t are different.
What does df stand for?
df stands for degrees of freedom.
How is df calculated for a single-sample design?
For a single-sample design, df equals n – 1.
What is Cohen's d?
Cohen's d is a measure of effect size that shows how much effect a treatment has.
What assumptions must be true for a single-sample t-test?
Subjects must be randomly sampled. 2. All scores must be independent. 3. The population must be normally distributed or n must be greater than 30.
What is pooled variance?
Pooled variance is a statistic that combines the variance of two samples together to provide a more reliable estimate.
What must be true for an independent-samples t-test?
Subjects must be randomly sampled. 2. All scores must be independent. 3. Two populations must be normally distributed or n1 + n2 > 40. 4. The two populations must have equal variances.
What is estimated standard error (s(M1 – M2))?
Estimated standard error indicates the typical distance between the difference of two sample means (M1 – M2) and the difference of their population means (μ1 – μ2).
What is a related-samples t-test?
A related-samples t-test is used when one sample of subjects provides two scores to analyze if the two population means are different.
What assumptions must be true for a related-samples t-test?
Subjects must be randomly sampled. 2. All difference scores must be independent. 3. The population must be normally distributed or n must be greater than 30.
What is standard error in relation to population means?
Standard error indicates the typical distance between a population mean (μ) and the mean of a sample (M) drawn from that population.
What does an interval estimate do?
An interval estimate provides a range of values within which the population parameter is thought to lie.
What is the conventional level of confidence for an interval estimate?
The conventional level of confidence is 95%.
What does '95% confidence' signify?
It signifies that if multiple samples are taken, 95% of the confidence intervals calculated will contain the actual population mean.
What is the purpose of ANOVA?
ANOVA is used to determine if there are significant differences among two or more population/treatment means.
What does it mean when ANOVA results are significant?
Significant results indicate that the differences between means are unlikely to have occurred by chance.
What should be done if the null hypothesis is rejected in ANOVA?
Further analyses, like posttests, should be performed to identify which means differ.
How is effect size measured in ANOVA?
Effect size is measured using eta squared (η2 = SSbetween / SStotal).
What does η2 indicate?
η2 indicates how much of the variability in the dependent variable is accounted for by differences between treatments.
What are the conventional values for η2 interpretation?
η2 values of .01, .09, and .25 correspond to small, medium, and large effect sizes, respectively.
What does MS between measure?
MS between measures the variance among group means.
What does MS within measure?
MS within measures the variance within groups.
Why is the F-ratio considered a ratio?
The F-ratio is considered a ratio because it is the ratio of the two mean squares (MSs).
How does the spread between group means affect SSbetween?
As group means get farther apart, SSbetween increases.
How does MSwithin change with score variability?
MSwithin increases as scores within groups become more spread out.
