The ____________________ and the ____________________ are the most commonly used inferential statistical tests for variables measured on an interval or ratio scale.
- Student’s T-test
- ANOVA
The _____________________ is used to evaluate hypotheses about the differences between two means.
Student’s T-test.
The ANOVA is preferred when more than two means are to be compared, in order to reduce the _________________________.
Experimentwise error rate.
The ______________________ is used when a study includes only one group and the group (sample) mean will be compared to a known population mean.
- Use:
- One IV: Single group
- One DV: Interval or ratio data
- Statistic: t
- df: (N - 1), where N = number of subjects.
Student’s t-Test for a Single Sample.
The ___________________________ is the appropriate statistical test when a study includes two independent groups and the means of the two groups will be compared.
- Use:
- One IV: 2 independent groups
- One DV: Interval or ratio data
- Statistic: t
- df: (N - 2), where N = total number of subjects
Student’s t-Test for Independent Samples.
The _______________________________ is used when the two means to be compared have come from correlated groups (e.g., a within-subjects design in which a single group of subjects will be compared to itself before and after the IV has been applied). Also appropriate when subjects have been matched on an extraneous variable and members of each matched pair have been assigned to a different group.
- Use:
- One IV: 2 correlated groups
- One DV: Interval or ratio data
- Statistic: t
- df: (N - 1), where N = number of pairs of scores
Student’s t-Test for Correlated Samples.
The _________________ is used when a study includes one IV and 2+ independent groups, and one DV that is measured on an interval or ratio scale.
- Use:
- One IV: 2+ independent groups
- One DV: Interval or ratio data
- Statistic: F
- df: (C - 1)(N - C), where C = number of levels of the IV and N = number of subjects
ANOVA.
As opposed to the t-test, the ANOVA enables a researcher to evaluate the relative contributions of different factors to the total amount of variability observed in a set of scores. This is done by “partitioning the ________________.”
Sum of Squares.
The one-way ANOVA divides the ___________ sum of squares (SST) into a ______________ sum of squares (SSB) and a _________________ sum of squares (SSW).
- Total
- Between-groups
- Within-group
SST = SSB + SSW
In an ANOVA, the sums of squares are converted to mean squares (variances) by dividing each sum of squares by the appropriate degrees of freedom (for the ANOVA, the df are used not only to identify the _________________, but to calculate the ___________).
- Critical value
- F-ratio
- Mean Square Total =
- Mean Square Between =
- Mean Square Within =
- MST = SST/df
- MSB = SSB/df
- MSW = SSW/df
______________ is a pooled measure of variability within each of the treatment groups, and is an estimate of variability due only to error; ____________ is a measure of variability between treatment groups, estimating the variability due to both error and the effects of the IV.
- MSW
- MSB
The F-ratio is calculated by dividing __________ by ___________.
F = MSB/MSW = (treatment + error)/error.
In an ANOVA, when H0 is true, MSB and MSW are _______________ and F = ___.
- The same
- 1
When the H0 is false, MSB is ___________ than MSW and F is ___ 1.
- Greater
- >
If a study includes more tha two groups, a statistically significant F indicates that there is some difference between the groups, but does not indicate which groups differ. ______________ tests are usually conduceted to ID which group means are significantly different.
- The _______________ can be used to make all pairwise and complex comparisons (Group 1 vs. Group 2; Group 1 vs. Groups 2 and 3, etc.)
- The _______________ to make pairwise comparisons when groups are of equal size
- Post-hoc
- Scheffe S test
- Tukey test
The ___________________ is an extension of the one-way ANOVA and is used when a study includes 2+ IVs. F-ratios are obtained for the main effects of each IV and their interactions.
- Use:
- 2+ IVs; Independent groups
- 1 DV; Interval or ratio data
- Statistic: F
Factorial Analysis of Variance.
The ________________________ is a type of factorial ANOVA that is employed when “blocking” has been used to control an extraneous variable. It involves treating the extraneous variable as an IV so that its main and interaction effects can be statistically analyzed. It also increases statistical power by reducing within-group variability.
Randomized Block ANOVA.
The ___________________ combines the ANOVA with regression analysis and allows an investigator to control an extraneous variable by statistically removing the portion of variability in the DV that is due to the extraneous variable. This reduces within-group variability, resulting in a more powerful test. It requires using subjects’ scores on the extraneous variable (the “covariate”) to adjust their scores on the DV.
Analysis of Covariance (ANCOVA).
The _____________________ is appropriate for studies using a within-subjects design in which the different levels of the IV or combinations of the levels of two or more IVs are sequentially administered to each subject.
Repeated Measures ANOVA.
The ___________________ is the appropriate test for studies using a mixed design in which at least one IV is a between-groups variable and one IV is a within-subjects variable.
Mixed (Split-Plot) ANOVA.
_____________________ is used when the study involves one or more quantitative IVs, and the researcher wants to evaluate the shape or form of the relationship between the IV and DV. The results indicate whether or not there is a statistically significant linear or nonlinear (quadratic, cubic, quartic) relationship between variables.
Trend Analysis.
The __________________ can be used when a study inclues one or more IVs and 2+ DVs that are each measured on an interval or ratio scale. It allows an investigator to simultaneously assess the effects of the IVs on all of the DVs and thereby helps control the experimentwise error rate.
Multivariate Analysis of Variance (MANOVA).
