Final Exam Flashcards
One-Way ANOVA: Testwise Type 1 Error Rate
α = .05
- 1 t-test
One-Way ANOVA: Experimentwise Type I error
rate
α ≤ k(k-1)/2
α = .15
- 3 t-tests
Relationship between mean
differences and variance
Use variance to define and measure the size of
the differences among the sample means
Logic of ANOVA
Partitioning variance into
between groups and within
groups (error) variance
Sources of between groups
variance
Sources of within groups
(error) variance
F-ratio under the null and
alternative hypotheses
Distribution of F-ratios under
the null hypothesis
ANOVA summary table and
knowing the relationships
between each value in the table
and the other values
The lower the degrees of freedom, the larger the value of F needed to be significant.
Effect size estimates
- Eta-squared
Multiple Comparison Procedures
- LSD vs. Bonferroni
Assumptions
Why include multiple IVs?
Factorial designs
Factors & levels
If Factor A has 3 levels and Factor B has 5 levels
then there are 3 x 5 combinations in a fully
crossed, factorial design.
– “3 by 5 factorial design”
Sources of variation in
factorial designs
Marginal means
the marginal means of one variable are the means for that variable averaged across every level of the other variable
Decomposing the total
variability
Additivity vs. interactivity
ANOVA summary table
Visually interpreting main
effects and interactions
Effect Size
Simple Effects
Relationship to relatedsamples t-test
Sources of variation
Using the interaction as the
error term
Assumptions
Sphericity
Testing for violations of
sphericity : Mauchly’s test
Correcting for violations of
sphericity
Multiple comparison (posthoc) procedures
Scatterplot
Direction, form, strength of
relationship between two
variables
Covariance
Pearson Correlation Coefficient
Hypothesis Test
Regression Line
Linear Equation
Least squares solution
- Total squared error
Regression: Hypothesis Testing
The analysis of variance differs from a t test for two independent samples because:
a) the t test is limited to 2 samples.
b) the analysis of variance can handle multiple samples.
c) the analysis of variance tests whether the samples have different variances.
d) both a and b
d) both a and b
In the analysis of variance we assume that:
a) the populations are normally distributed.
b) the populations follow a rectangular distribution.
c) the populations all have completely different distributions.
d) There is no assumption about the distribution of the population.
a) the populations are normally distributed.
Error variance in the analysis of variance is estimated by:
a) differences between subjects in the same group.
b) differences between subjects in different groups.
c) the overall variability of scores in the experiment.
d) the misrecording of data
a) differences between subjects in the same group.
If the null hypothesis in the analysis of variance were true,
a) the variances would all be the same.
b) the sample means would all be the same.
c) the population means would all be the same.
d) every subject would have the same score.
c) the population means would all be the same
Fisher’s LSD test is most useful when:
a) you have only one mean.
b) you have three means.
c) you have more than three means.
d) you have a nonsignificant overall F
b) you have three means.
The familywise error rate is:
a) the probability of at least one Type I error in a set of comparisons.
b) the probability of no Type I errors.
c) the number of Type I errors that you are likely to make.
d) the probability of a Type II error.
a) the probability of at least one Type I error in a set of comparisons.
The difference between a one-way analysis of variance and a factorial analysis of
variance is:
a) the presence of a test for an interaction.
b) the presence of tests for more than one main effect.
c) one-way analyses of variance have an error term, whereas factorial analyses do not.
d) both a and b
d) both a and b
A simple effect is calculated by:
a) looking only at the data for one level of one of the independent variables.
b) averaging across the levels of one of the independent variables.
c) ignoring one of the independent variables.
d) dividing the main effect by the degrees of freedom.
a) looking only at the data for one level of one of the independent variables
A pediatrician is studying weight gain in infants. He divides them into 2 groups: breast
fed and bottle fed. Further, he divides them into those whose mothers feed them on a
timed schedule, and those whose mothers feed them when they cry (on demand). Weight
gain is the dependent measure. What type of analysis should pediatrician conduct on the
data?
a) a regression
b) a one-way ANOVA
c) a 2 X 2 factorial ANOVA
d) a 2 X 2 correlation
c) a 2 X 2 factorial ANOVA
The major disadvantage with repeated-measures designs is that they:
a) require too many subjects.
b) are less powerful than between-subjects designs.
c) have a funny looking summary table.
d) are subject to the influence of carry-over effects.
d) are subject to the influence of carry-over effects.
The correlation between two variables is defined as:
a) the covariance of those variables divided by the product of their standard deviations.
b) the covariance of those variables divided by the variance of X.
c) the covariance of those variables divided by the variance of Y.
d) the cross-product of all of the pairs of scores.
a) the covariance of those variables divided by the product of their standard deviations.
If the correlation between the rating of cookie quality and cookie price is .30, and the
critical value from the table of significance of correlation coefficients is .35, we would
say that:
a) the correlation is not statistically significant.
b) the correlation is statistically significant.
c) the difference is too close to call.
d) we don’t have any way to come to a conclusion
a) the correlation is not statistically significant.
When we say that a correlation coefficient is statistically significant, we mean that:
a) we have reason to believe that it reflects an important relationship between variables.
b) we have reason to believe that the relationship is positive.
c) we have reason to believe that the true correlation in the population is not 0.0.
d) we have strong support for a causal statement about the relationship
c) we have reason to believe that the true correlation in the population is not 0.0.
The correlation in the population is denoted by:
a) p
b) r
c) R
d) theta
a) p
The covariance between height and running speed on the State College track team was
equal to –28.21. This tells us that the:
a) relationship between height and speed is significant.
b) relationship between height and speed is negative.
c) the correlation is equal to the square root of –28.21.
d) the correlation is equal to –28.21.
b) relationship between height and speed is negative.
Which r-value represents the strongest correlation?
a) +.50
b) -.50
c) -.75
d) 1.65
c) -.75
A correlation was computed between amount of exercise people do and people’s overall
happiness. A significant correlation was found, such that the more people exercise, the
happier they are. What is the best conclusion to draw from this finding?
a) Exercise leads people to be happy.
b) We have proved that people should exercise more.
c) A positive relationship exists between exercise and happiness.
d) A negative relationship exists between exercise and happiness.
c) A positive relationship exists between exercise and happiness
We want to demonstrate that a relationship exists between optimism and happiness. We
are not concerned with trying to demonstrate that one variable causes the other. What
type of statistical test can be used to see if a relationship exists between the variables?
a) correlation
b) independent samples t-test
c) power analysis
d) one way ANOVA
a) correlation
