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PSYC 3000 Study Guide - Analysis Of Variance


Department
Psychology
Course Code
PSYC 3000
Professor
Bruce Hutcheon

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In a 1-way within-subjects ANOVA the sum-of-squares term quantifying the stable differences between participants is calculated using all the observations in the entire design. T In a 2-way
within-subjects design, if both variables have 5 degrees of freedom, then the degrees of freedom for their interaction is 10. F [levels a x levels b, 5x5=25] When considering the main effect of
treatment A in a 2-way ANOVA, the larger the standard deviation of the marginal means for treatment A, the larger the effect size, fA. T The dependent variable in a within-subjects ANOVA is
assumed to be nominal data. F[interval] For a test that the correlation coefficient in the population os zero, you can increase the power of the tests by increasing n. T For a 2-way within-
subjects ANOVA, the main effects of the treatments and the interaction are all tested using different MSError terms. T[each treatment has own error] For a 2-way mixed-factors ANOVA, the
main effects of the treatments and the interaction are all tested using different MSError terms. F For a 2-way mixed-factors ANOVA, if you know only the values of a, b, and n, then it is still
possible to calculate the between-subjects dfError. F For a 2-way within-subjects ANOVA, if you know the values of a, b, and n, then it is still possible to calculate the between-subjects dfError.
T In a 2-way within-subjects design, the number of possible simple effects that can be tested is a times b. F[a+b] The maximum value of
2 is 1. T [0-1] For treatment A in a
2-way design, the value of
2
partial A
is always greater than or equal to the value of
2
A
. T [denominator decreasing] For a 1-way design, the value of
2 does
not depend on whether you perform a within-subjects or between-subjects analysis. T The minimum value for Cohen’s f is 0.T[no neg. values] A large Cohen’s effect
size, f, for an ANOVA means that the null hypothesis will be rejected. F If the regression slope for a bivariate dataset is positive then the correlation coefficient will be
positive too. T The larger the sample size, the smaller the standard error of the regression slope. T The larger the slope of the regression line, the greater the proportion
of explained variation. F[unrelated]
2 and r2 are similar in that they both represent the proportion of unexplained variation in a dependent variable.F[explained]
2
and r2 are similar in that they both represent the proportion of explained variation in a dependent variable. T
bivariate dataset with n = 5 and r = 0.5 What is the standard error of the correlation coefficient, sr, estimated from this sample? sr = ½ What is the t-value in a test that the sample correlation
coefficient is significantly different from zero? t = 1 How many degrees of freedom does the t-value in the previous question have? 3bivariate dataset with n = 5, s
= 40, sX = 2, and b =
30What is the standard error of the regression slope, sb, estimated from this sample? sb = 10 What is the t-value in a test that the sample regression slope in the population is b* = 20? t = 1
What is the t-value in a test that the sample regression slope in the population is b* = 0? t = 3 Researchers are interested in the role of blood sugar[interval] in cognitive performance in
the elderly. They have 10 elderly participants drink a glass of an orange-flavoured juice sweetened with glucose to raise their blood sugar levels. For each question, state what test
you would use to determine the association between blood sugar levels and cognitive performance. Each participants is given a difficult cognitive task to perform and the order in which
they finish is recorded. The independent variable is the participant’s actual blood sugar level when undertaking the task. Non-parametric correlation Each participant is given a difficult
cognitive task to perform and the time needed to finish is recorded. The gender of the participants is recorded as is whether or not they are diabetic. Factorial ANOVA[2 categorical IV,
interval DV] Each participant is given a difficult cognitive task to perform and the time needed to finish is recorded. The independent variable is the participant’s actual blood sugar level when
undertaking the task. Correlation[2 interval] How many different alpha terms exist in the structural model for a 2-way design with a=3 and b=4? 3How many different beta terms exist in the
structural model for a 2-way design with a=3 and b=4?4 How many different "alphabeta" terms exist in a 2-way design with with a=3 and b=4?12 Which of the following terms are used in
calculating the main effect of treatment A for a 2-way Squared deviations of marginal means of A from the grand mean Which of the following characterizes the "alpha_k" terms that appear in
the structural model for a 2-way design? Differences between marginal means for treatment A and the grand mean Which of the following characterizes the "beta_j" terms that appear in the
structural model for a 2-way design?Differences between marginal means for treatment B and the grand mean For a given set of observations in a 1-way design, the SS_Error term that appears
in an independent-samples analysis of those observations will be smaller than either of the SS_Error terms that appear in a repeated-measures analysis.False For a given set of observations
conducted in a 1-way design, the value of SS_Treatment is the same in an independent-samples analysis and a dependent-samples analysis.True In a dependent-factors analysis, the smaller the
value of the SS_Error derived from individual differences, the greater the chance that the treatment will be found to have a significant effect on the dependent variable.False.What terms should
be squared and summed to form SS_Subjects in a 1-way repeated-measures analysis? Deviations of subject means form the grand mean The larger the standard deviation of errors around the
regression line, the less likely it is that the regression slope, b, will be significantly different from zero True Suppose you are studying the relationship between mathematical skill and verbal
skill. If you collect data from students in two different elementary schools and find that the regression slope, b, for school 1 is twice as large as for school 2, this means that the regression slope
for school 1 is more likely to be significantly different from zero. False Suppose you are studying the relationship between mathematical skill and verbal skill. If you collect data from students
in two different elementary schools and find that the correlation coefficient, r, for this relationship in school 1 is twice as large as for school 2, this means that the correlation coefficient for
school 1 is more likely to be significantly different from zero.False The regression slope in the previous question was negative. Does this mean that nonsense words with many letters, or only a
few letters, are remembered longer?Nonsense words with only a few letters are remembered longer than nonsense words with many letters In the question about the dependence of word
memory on word length, what value would the regression slope be if the dependent variable (time for accurate recall of a nonsense word) was measured in hours instead of days? b = -6 In the
question about the dependence of word memory on word length, the predicted duration of memory for a word 13 letters long is -0.25 days. What does this mean The linear relationship between
memory duration and word length found for the original dataset does not generalize well to extremely long word lengths outside the original dataset. How many degrees of freedom are
associated with a test to determine if an observed regression slope is equal to a hypothesized value?Number of bivariate observations minus 2 For the results in question 3, what the proportion
of variation in the dependent variable that is exclusively explained by whether or not participants were violent offenders independent of what level of training they received? 4/46 The
proportion of the variance in Y values accounted for by the variance in X is given by r-squared. True Suppose you have a bivariate dataset consisting of the following X-Y pairs...(1, 7), (2, 8),
(6, 9). Which of the following points is on the regression line for the regression of Y on X? (3, 8) For the bivariate dataset consisting of the X-Y pairs (1,1) (2,2) (3,3), what is the sum of squared
errors?0 Find the proper way to end the following sentence. "The line for the regression of Y on X is found by minimizing the..."the sum of the squared differences between the actual and
predicted Y values If 2 bivariate datasets have the same correlation coefficient, then their respective regression lines explain the same proportion of Y variation. True Imagine 2 bivariate
datasets having the exactly same regression line (i.e., same intercept and same slope). In the first dataset the residual errors around the regression line are small, so that almost all the
datapoints lie directly on the line. In the second dataset the residual errors are large so that the data appear to form a cloud around the regression line. Since the 2 datasets have the same
regression slope they have the same correlation coefficient. FalseSuppose that when 2 bivariate datasets are plotted, the datapoints and regression lines look identical. This means that the
regression slopes are the same.False Suppose that when 2 bivariate datasets are plotted, the datapoints and regression lines look identical. This means that the correlation coefficients are
the same.True The correlation coefficient for a bivariate dataset is the value of the regression slope that you would find for the data after z-transforming all the X values and all Y
values.TrueThe correlation coefficients of a bivariate dataset is the value of the slope of the regression line found after first z-transforming all the X values and all the Y values. What is the
value of the intercept of the regression line found after z-transforming all the X values and all the Y values?0 The correlation coefficient, r, for a bivariate dataset remains unchanged if all X
values are multiplied by 2.TrueFor a bivariate sample, the larger the standard deviation of X values the more accurately the regression slope reflects the true regression slope in the
population.True Why is SS_Subjects in a 1-way repeated, measures ANOVA thought of as an error term?It corresponds to differences between individuals and these differences cannot be
explained by differences in treatment Suppose that a 2-way between-subjects ANOVA is conducted and it is found that SSA = 10. Now suppose that, subsequent to this, it was realized that
the data actually come from a 2-way within-subjects design. If the same experimental results are reanalyzed, what will happen to the value of SSA? It will stay the same How many
participants are there in a 2-way repeated-measures design if the number of levels of treatment A is “a”, the number of levels of treatment B is “b”, and the number of observations per cell
is n? n In a within-subjects 2-way factorial design, what degrees of freedom should be used for the between-subjects error?n-1 In a mixed-factors 2-way factorial design in which the within-
subjects factor is factor B, what degrees of freedom should be used for the between-subjects error?(an-1)-(a-1) For a between-subjects 2-way ANOVA, the main effects and simple effects of
all treatments are tested using the same MSError. True What is the value of the between-subjects dfError for a 2-way mixed-factors ANOVA with a=10, b=3, and n=5? Cannot be calculated
with this information In a 2-way between-subjects ANOVA, how do you compute the sum-of-squares for the main effect of treatment B?Sum of squared deviations of marginal means for B
from the grand mean Researchers are interested in the effectiveness of a reading skills course for primary school children. They recruit 100 children and assess their reading comprehension
before and after the children receive a specially designed 2-month course. In addition the researchers keep track of the gender of the children (assume this is a balanced design). What sort
of test should be used to analyze the results from this experimental design?mixed-factors 2-way ANOVA What sort of test would you use to analyze the simple effect of gender on reading
comprehension before children receive the specialized reading course?Independent-samples t-test For a particular set of results in a 2-way design, the value of is greater than or equal to the
value of partial.FalseFor any particular set of observations in a 2-way design, the value of the overall is greater than the value associated with either of the main effects or the interactionTrue
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