Review Outline and Review Activity – Exam 3 – Psy 340
Fall 2009
Reminder! Exam 3 is during our scheduled final exam time…
Chapter 10: Factorial ANOVA (ignore calculation sections of this chapter…focus on concepts)
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Why is this an efficient research design? Examining 2 or more variables’ effect on DV at once
What does an interaction effect mean? Be able to interpret one given the variables’ meaning.
A 2-way ANOVA as an example of factorial design:
o 2 possible main effects (1 for IV 1, 1 for IV2)
o 1 possible interaction (between IV1 and IV2)
o 2x2 tables may help you notice/interpret main effects (seen by marginal means) and
interaction effects (seen by pattern of differences in cell means – that is, in direction
and/or magnitude of row differences)
Be able to look at a 2x2 table and have an idea of whether there might be main effects and/or
interactions
Alternately, be able to look at a graph and tell whether there is an interaction (is there a crossover effect? Is the magnitude of the differences in IV2 the same or different for the different
levels of IV1)?
Be able to interpret SPSS output for 2-way ANOVA – is the F test for Main Effect 1 significant?
For main effect 2? For the interaction?
Chapter 11 – Correlation
 What is a correlation? What information does it provide?
 What are the interpretations of negative and positive correlations?
 Calculate a Pearson’s correlation coefficient (r; will be given the formula)
 Issues in interpreting correlations:
o significance (what does it mean for a correlation to be significant?)
o squaring the correlation (r-squared) gives you the proportion of reduction in error (aka
proportion of variance in y accounted for by x)
o problems interpreting correlation coefficients due to range restriction (what does range
restriction mean? When/how does it create problems?)
o Interpreting the size of correlations (Cohen’s guidelines)
SPSS Output for Correlations:
Be familiar with the interpretation of SPSS correlation output. Specifically,
In SPSS output, to find the correlation between x and y, follow the row for ‘x’ to the column for ‘y’
and you will find 3 lines of information:
 First line gives the actual correlation (labeled “Pearson correlation”)
 Second line gives p value (significance) of correlation. If p < .05, it is significant
 Third line gives sample size used to compute the correlation.
Chapter 12 – Regression
 Distinction between a predictor and a criterion variable (be able to identify which is which if
given an example research question)
 Raw score Prediction model – this is the model where you calculate a (regression constant) and b
(regression coefficient).
o What is the interpretation of a (the regression constant) and b (regression coefficient or
slope)?
 The model is,
o ŷ = a + b (x)
If given a regression equation, you should be able to identify which number is a and which is
b and interpret each. For example, if ŷ = .87 + 2.56(x), know that .87 is the regression
constant where the regression line crosses the y axis (interpretation = y equals .87 when x =
0); and know that 2.56 is b, the slope of the regression line (interpretation = we’d expect an
increase of 2.56 points in y for a 1 point increase in x).
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Regression line – use the regression equation (prediction model) to find predicted y scores for each
person who has an x score. For each person, graph (x, ŷ) – that is, their actual x score against their
predicted y score. You’ll see that the slope should match b and the y intercept should be equal to a.
o You can randomly choose a few x values to put into the regression equation and find the
predicted y score that corresponds to each x. Then plot each of those (x, ŷ) points for your
regression line.
o You can also use (Mx, My) as a point because the regression line will always go through the
two means (of x and y).
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Proportionate Reduction in Error (PRE)
o Conceptually, the PRE tell us how good our regression equation/line is at predicting y scores.
It may be the case that the predictor we chose (x) is very accurate and strongly related to y, so
it does a good job of predicting y scores (that is, when a new sample is later measured on y,
the predicted y scores came very close to actual y scores). It may also be the case that the
predictor did not do a very good job of predicting y scores.
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We need PRE as an index of how good our regression line is compared to a mean (baseline)
model. That is, if we had no predictor to use in predicting a y value for someone, we could
always just predict that they would score at the mean of y. In the mean (baseline) model, we
would predict that everyone would score at the mean of y. Obviously, this will almost never
be the case, so this probably isn’t a great model. But it does serve as a comparison for our
regression model.
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PRE is based on two components – Sum of Squares Error (SS error) and Sum of Squares
Total (SS total). The SS error component is an index of error made by our regression
equation/line when predicting y using ŷ. The SS total component is an index of error made by
the mean (baseline) model when predicting y using My.
SS error = Σ (y – ŷ)2
SS total = Σ ( y – My)2
PRE = SS total – SS error
SS total
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You can convert this to a percentage and it tells you how much better your
regression equation is over a mean (baseline) model. If PRE = .85, then the
regression equation reduces error by 85% over the mean (baseline) model.
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Note: PRE is equal to r2
Multiple Regression:
 What is the difference between standardized and unstandardized regression coefficients?
When it is more appropriate to use standardized?
 Multiple regression model with 3 predictors, using standardized (beta) coefficients:
Yˆ  a  (1 )( X1 )  ( 2 )( X 2 )  (3 )( X 3 )
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How do we interpret beta?
What are some of the hypothesis tests you could use for multiple regression?
o Is beta significantly different from 0? (if so, what does this tell us?)
SPSS Output for Regression: be familiar with how to interpret regression output (you have a handout
highlighting the important pieces of the output).
Look for r2 at the beginning of the output.
Go to the section labeled “Coefficients” to find the pieces for the regression equation. “Constant”
indicates a; b or beta should be indicated in a separate row labeled with the name of your predictor. Be
able to use these pieces of information to write out the regression equation.
Chapter 13 – Chi-square tests
 Chi-square ‘goodness of fit’ test deals with one nominal/categorical variable
o What does the null hypothesis state? Research hypothesis?
o Compare observed (O) frequencies with expected (E) frequencies
 How do we find Expected frequencies? Can either use equal distribution across
all categories or use a theory based on a comparison population.
 Using the chi-sq formula – is the ‘mismatch’ between O and E larger than
expected by chance?
 Compare to chi-sq critical and determine whether to reject/fail to reject null
 Interpretation if we reject the null?
 Chi-sq ‘test for independence’ deals with two nominal/categorical variables
o Is there any relationship between the two variables? Construct contingency tables
o What is the null hypothesis? Research hypothesis?
o Find Expected (E) frequencies for each cell in contingency table
 Assuming null hypothesis is true.
 See formula for determining “E” for each cell
 See chi-square formula and find chi-sq critical value
 Decision rule – reject or fail to reject null?
o What is the interpretation if we reject the null?
 SPSS for chi-square test for independence (under ‘Descriptives’  “Crosstabs”)
o See class example and notes for how to interpret.
Chapter 15 – General Linear Model (concepts only, skip the calculations)
 What is the GLM?
 Understand the hierarchy of statistical techniques: Multiple regression is most general,
Correlation & ANOVA are special cases of multiple regression; T-tests are special cases of
correlation & ANOVA.
 How is the GLM similar to and different from the multiple regression model?
 How are t-tests and F tests similar/related? Can one be found from the other?
 How is a significance test for a correlation related to a t-test?
REVIEW ACTIVITY:
Chapter 10:
Set 1, #2 all parts
Be familiar with SPSS output for 2-way ANOVA (examples from either in class, homework, or final
project!). Check two main effects and one interaction. Examine follow-up tests to determine which
groups differ significantly and how the interaction should be interpreted (if significant)
Chapter 11:
Set 1, #4
Review SPSS output for correlation.
Chapter 12:
Set 1, #4 parts a, b, c, d, e, and k
Review SPSS output for multiple regression. Be familiar with R2, betas, and how to write the final
regression equation.
Chapter 13:
Set 1, #4 a only, and 6 a only
Chapter 15: no calculation or SPSS problems for this chapter.