Chapter 10: Independent Samples Flashcards
What are two sample hypothesis tests used to make?
statistical decisions about relationships between two variables
What comparisons can be made?
Two parameters to see whether they are equal
What questions should you ask yourself?
Are they unequal enough to be statistically significant, Can we reject null that the two stats are equal and represent separate pops
What can both z-tests and t-tests be used for comparing?
Means of interval and ratio level variables
What are between groups comparisons?
determine if a difference between two groups is large enough to be statistically significant
What is statistically significant?
Is difference large enough that we can reject null of no difference
What determines the approach?
Size of samples, level of measurement, whether samples are IV or DV, whether variances of independent samples are equal, whether sd of pop is known or sd is used to estimate it
What can z-tests be used to compare?
Proportions of nominal and ordinal variables
What do independent samples have?
No overlap, mutually exclusive groups
What do dependent samples have?
Some sort of overlap
In regard to samples what could two data points have?
Two data points for same person, pairs of data points for two people who are matched
What measurement of variables can be analyzed using t-tests?
Interval and ratio
What is the main difference between independent samples and dependent samples?
Independent are mutually exclusive, dependent samples have some overlap or connection to each other
What is the book definition of between-groups comparisons?
Data from independent samples
What type of data do within-group comparisons use?
Dependent samples
What is standard error?
Probability distribution is created for many values of means from many different samples
What happens as the size of the samples increase?
Standard error becomes smaller
What does the standard error becoming smaller indicate about the size of the sample?
Little variation around the population mean, smaller the standard error the more precise the estimate of the pop mean
What happens if one or both sample has a sample less than n=30?
Use a t-test instead
What does a t-test graph look like with smaller samples?
Relatively flat
What does a t-test with a standard sample look like?
Very close to normal
What happens with sample size and using a z-test or t-test to define which one?
Both samples must meet the same criterion for the test that is going to be used
What happens if one variance is no more than twice the other?
They are considered approximately equal and a pooled estimate of the standard error can be used
What is an explanation of the formula for pooled variance?
s21 and s22 are the sample variances (not standard deviations) and n1 and n2 are the sizes of the two samples (1 and 2). The square root is taken to complete the calculation as the estimate of the pooled standard deviation.
What happens if the variances are not equal to each other?
Unpooled standard error is used
Why can’t you use the pooled variance for unequal variances?
Because it can lead to unreliable results with the t-test
What is “too different” defined as?”
One variance more than twice the other
How to determine degrees of freedom from approximately equal variances?
determined by summing the sample sizes and then subtracting the number of samples
What is the formula for approximately equal variances?
(n1 + n2) - 2
What does the value for d tell us?
Mean difference between the two groups
Can spooled by calculated using the sample size and standard deviations from the samples?
Yes
Given the same t-statistic and same variances, a hypothesis test based on larger sample would likely show a smaller effect size?
No
What are independent samples?
Selection of elements in one sample are not influenced by selection of elements in the other sample
How to find df is the test has two samples?
Add the two degrees of freedom together
What are the assumptions for independent sample t-tests?
Random sampling methods, sampling with replacement, normally shaped,
