T-Tests, ANOVAS, ANCOVAS Flashcards
T-Tests are:
- Test whether the regression coefficient (b), is significantly different from zero
- Provides some idea of how well a predictor predicts the outcome variable
- Can be used to see whether a predictor variable makes a statistically significant contribution to the regression model
Independent T-Test
Tests for differences between means of groups containing different participants when the sampling distribution is normal, the groups have equal variances and data are at least interval
Paired Samples T-Test
- Same participants take part in both experimental conditions
- Ought to be less unsystematic variance compared to the independent t-test
- Other things being equal, you do not need as many participants as you would for an independent samples design
T Distribution becomes closer to normal when…
Degrees of freedom increase
One-Sample T Test Assumptions
IV is continuous, independent scores, normal distribution, homogeneity of variances
One- Sample T Test
Compares the mean of the sample data to a known value (IQ of class compared to IQ of society)
Independent Sample T-Test Assumptions
Independence of groups, normal distribution, equal variances, homogeneity of variances, DV is interval or continuous, IV is categorical
Independent Samples T-Test
Most common form of T Test
Compares the differences between the means of groups containing different participants when the sampling distributions is normal, the groups have equal variances, and data are at least interval
Paired T Test Assumptions
DV is continuous, related samples, normal distribution
Paired T Test
Compares the means between two related groups on the same continuous, dependent variable (same group will be used in both trials)
ANOVA stands for…
Analysis of variance
When should ANOVA be used?
if you are comparing more than 2 groups
Family Wise Error
alpha level is our probability of rejecting the null hypothesis when the null hypothesis is true
How can you avoid/minimise family wise error?
adjusting the alpha level by (finish on slide)
Bonferroni test, tests what?
Guarantees control over type 1error, test to investigate which groups differ in a 1-way ind ANOVA
When the between-groups variance is a lot larger than the within-groups variance, the F-value is ____ and the likelihood of such a result occurring because of sampling error is _____
large; low
Imagine you compare the effectiveness of four different types of stimulant to keep you awake while revising statistics using a one-way ANOVA. The null hypothesis would be that all four treatments have the same effect on the mean time kept awake. How would you interpret the alternative hypothesis?
At least two of the stimulants will have different effects on the mean time spent awake
An experiment was done to look at whether different relaxation techniques could predict sleep quality better than nothing. A sample of 400 participants were randomly allocated to one of four groups: massage, hot bath, reading or nothing. For one month each participant received one of these relaxation techniques for 30 minutes before going to bed each night. A special device was attached to the participant’s wrist that recorded their quality of sleep, providing them with a score out of 100. The outcome was the average quality of sleep score over the course of the month.
Which test could we use to analyse these data?
Regression or ANOVA
Differences between group means can be characterized as a regression (linear) model if:
The experimental groups are represented by a binary variable (i.e. code 1 and 0).
Other things being equal, compared to the paired-samples (or dependent)t-test, the independent-test:
Has less power to find an effect.
Standard error…
It is the standard deviation of the sampling distribution of a statistic
In t-distribution, as the df increase the distribution becomes closer or further away from normal
closer
Partial eta squared is reported for…
ANOVA and ANCOVA
Assumptions of ANOVA
- Independence of data
- DV is continuous, IV is categorical
- No significant outliers
- DV is approximately normally distributed for each category of the IV
ANCOVA is an extension of…
Multiple Regression
ANCOVA allows you to test…
All the regression lines to see which have different intercepts as long as all your slopes are equal
Unlike an ANOVA and ANCOVA also…
- Controls for covariance
- Studies combinations of categorical and continuous variables, the covariate becomes the variable of interest RATHER than the one you control
In a study where we test if technique has an impact on exam scores, but we want to account for the students current grade what is the covariate?
The current grade
Assumptions of ANCOVA
1.Independent variablesshould becategorical variables.
2. Thedependent variableand covariate should be continuous variables(measured on aninterval scaleorratio scale.)
3. Make sureobservations are independent - don’t put people into more than one group.
4. Normality: the dependent variable should be roughlynormalfor each of category ofindependent variables.
5. Data (and regression slopes) should showhomogeneity of variance.
6. The covariate and dependent variable (at eachlevelof independent variable) should belinearly related.
7. Your data should behomoscedastic
8. The covariate and theindependent variableshouldn’t interact.In other words, there should be homogeneity of regression slopes.
What do we partition in an ANCOVA?
Total variance into IV, DV, and covariate
What do we partition in an ANOVA
Total variance into IV and DV
Dummy Variables in an ANOVA
Binary value (0 or 1)
Control is always 0
One value will be 1 the other 0, they will not both be one
