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t-test for Two Related Samples - Coggle Diagram
t-test for Two Related Samples
Repeated measures design or within-subject design
A research design that uses the same group of individuals in all of the different treatment conditions.
Structural similar to the other t statistics we have examined
Difference scores, or D values
Difference between the first score and the second score
The sample of difference scores (D values) serves as the sample data for the hypothesis test and all calculations are done using the D scores.
difference score= D=X2-X1
MD is the mean for the sample of D scores MD= Sum of the difference / # of participants
Single-Sample : t= Sample mean- population mean/ sm
Repeated-Measures: t= sample mean difference- population mean difference / sMd
Assumptions
2) The population distribution of difference scores (D values) must be normal.
1) The observations within each treatment condition must be independent. Inside each treatment, the scores are obtained from different individuals and should be independent of one another
Sample Variance & Sample Size
Variablility
Sample variability describes the consistency of the treatment. ex: a treatment consistently adds a few points to each individuals score, then set of difference scores will be clustered together with relatively small variability
Repeated Measures vs Independent Measures
Number of Subjects: repeated-measures design typically requires fewer subjects than an independent-measures design. Uses particpants
Study Changes over time: Well suited for studying learning, development, or other changes that take place over time.
Individualy differences: are characteristics such as, IQ, gender, and personality that vary from one individual to another
Power: Repeated-measures tends to have more power than independent measures design
Time-Related factors and order effects
Counterbalancing: the goal is to distribute any outside effects evenly over the two treatments
Each individual is measured in two different treatment conditions, often at two different times. Changes in scores that are caused by participation in an earlier treatment are called order effect and can distort the mean differences found in repeated-measures research studies
Matched-subjects design: each individual in one sample is matched with an individual in the other sample. The matching is done so that the two individuals are equivalent (or nearly equivalent) with respect to a specific variable (or variables) that the researcher would like to control.
The standard error is inversely to sample size (larger size leads to smaller error) and is directly related to sample variance (larger variance leads to larger error). As a result, bigger sample produces a large value for t-statistic (further fro zero) and increases the likelihood of rejecting Ho