Please enable JavaScript.
Coggle requires JavaScript to display documents.
THE t-TEST FOR TWO INDEPENDENT SAMPLES - Coggle Diagram
THE t-TEST FOR TWO INDEPENDENT SAMPLES
INDEPENDENT MEASURES RESEARCH DESIGN:
emphasize the fact that the design of the study involves separate and independent samples and makes a comparison between two groups of individuals.
BETWEEN SUBJECTS DESIGN:
another way to describe independent measures research design; a research design that uses a separate group of participants for each treatment condition (or for each population)
REPEATED MEASURES RESEARCH DESIGN:
strategy in which two sets of data are obtained from the same group of participants
WITHIN SUBJECTS DESIGN:
another way to describe related measures research design; the second research strategy, in which the two sets of data are obtained from the same group of participants,
THE FORMULAS FOR AN INDEPENDENT-MEASURES HYPOTHESIS TEST:
The independent-measures hypothesis test uses another version of the t statistic.
SINGLE SAMPLE
T STATISTIC:
the original formula
INDEPENDENT MEASURES T STATISTIC:
the new formula
ESTIMATED STANDARD OF DIFFERENCE BETWEEN TWO SAMPLE MEANS:
difference between two sample means t
INDEPENDENT-MEASURES t:
basically a two-sample t that doubles all the elements of the single-sample t formulas.
POOLED VARIANCE:
method correcting bias in standard error by combining two sample variances into a single value
EQUAL SAMPLE SIZES:
pooled variance is exactly halfway between the two sample variances. Because the two samples are exactly the same size, the pooled variance is simply the average of the two sample variances.
UNEQUAL SAMPLE SIZES:
the pooled variance is not located halfway between the two sample variances. Instead, the pooled value is closer to the variance for the larger sample than to the variance for the smaller sample.
DIRECTIONAL HYPOTHESIS AND ONE-TAILED TESTS:
When planning an independent-measures study, a researcher usually has some expectation or specific prediction for the outcome
STEP 2:*
locate the critical region; computation of the sample variance for each of the separate samples
**STEP 3:
calculate the data and calculate the test statistic
STEP 1:
state the Hypotheses and select the alpha level; computation of the sample variance for each of the separate samples
STEP 4:
make a decision
ASSUMPTIONS OF UNDERLYING THE INDEPENDENT-MEASURES t FORMULA:*
there are three assumptions that should be satisfied before you use the independent-measures t formula for hypothesis testing
FIRST ASSUMPTION:
the observations within each sample must be independent
SECOND ASSUMPTION:
the two populations from which the samples are selected must be normal.
THIRD ASSUMPTION:
the two populations from which the samples are selected must have equal variances.
HOMOGENEITY OF VARIANCE:
the two populations being compared must have the same variance.
TWO POINTS FOR ESTIMATED STANDARD ERROR:
to develop the formula for standard error we consider two points
POINT 1:
each of the two sample means represents its own population mean, but in each case there is some error.
POINT 2:
for the independent-measures t statistic, we want to know the total amount of error involved in using two sample means to approximate two population means
HARTLEY'S F-MAX TEST: formula used to check whether two populations being compared have the same variance