08 Oct Logistic Regression
Logistic Regression
Logistic regression is used when you want to
Predict a continuous variable from dichotomous ones.
Predict a dichotomous variable from continuous or dichotomous variables.
Predict any categorical variable from other categorical variables.
Predict a continuous variable from dichotomous or continuous variables.
Which of the following statements is not true about the Wald statistic?
The Wald statistic assesses the individual contribution of a predictor to a logistic regression model.
The Wald statistic tends to be biased when the regression coefficient is large.
If the Wald statistic is equivalent to the t-statistic in multiple regression?
The Wald statistic has a t-distribution.
A researcher was interested in predicting whether a person would attempt to commit suicide (score = 1) or not (score = 0) from their depression scores. They found that the value of exp b was 2.56. How should this value be interpreted?
If two people have depression scores that differ by 1 unit, then the odds of the person with the higher score attempting suicide are is 2.56 higher than for the other person.
2.56 times more people who attempted suicide scored highly on depression.
If two people have depression scores that differ by 1 unit, then the odds of the person with the higher score attempting suicide are is 2.56 lower than for the other person.
Suicide rates are 2.56 times as high in depressed people.
The odds of an event are:
The ratio of the probability of an event not happening to the probability of the event happening.
The ratio of the probability of an event happening to the probability of the event not happening.
The probability of an event occurring.
None of the above.
What does logistic regression NOT do?
predicts a dependent variable on the basis of several independent variables
determines the variance in the dependent variable explained by the independent variables
ranks the relative importance of independent variables
assesses the impact of covariate control variables.
Chapter 7 – Comparing the two means
A researcher was interested in stress levels of lecturers during lecturers. She took the same group of 8 lecturers and measured their anxiety (out of 15) during a normal lecture and again in a lecture in which she had paid students to be disruptive and misbehave. Based on the SPSS output how would you interpret these results?
Paired Samples Test
Paired Differences
t
df
Sig. (2-tailed)
Mean
Std.
Deviation
Std. Error Mean
95% Confidence
Interval of the Difference
Lower
Upper
Pair Misbehaved – Normal
1 Lecture
6.2500
4.8033
1.6982
2.2344
10.2656
3.680
7
.008
Anxiety levels were significantly lower in lectures in which students misbehaved.
There were no significant differences between anxiety levels in normal lectures and in those in which students misbehaved.
Anxiety levels were significantly higher in lectures in which students misbehaved.
We can’t tell any of the above from the output given.
A psychologist was interested in whether there was a gender difference in the use of email. She hypothesised that because women are generally better communicators than men, they would spend longer using email than their male counterparts. To test this hypothesis, the researcher sat by the email computers in her research methods laboratory and when someone started using email, she noted whether they were male or female and then timed how long they spent using email (in minutes). What should she report?
Group Statistics
Gender
N
Mean
Std. Deviation
Std. Error Mean
Time Using Email (Day 2) Male
Female
8
8
5.0000
32.0000
4.50397
40.04640
1.59239
14.15854
Independent Samples Test
Levene’s Test for Equality of Variances
t-test for Equality of Means
F
Sig.
t
df
Sig. (2-tailed)
Mean Difference
Std. Error Difference
95% Confidence Interval of the
Difference
Lower
Upper
Time Using Email (Day 2) Equal variances
assumed
12.999
.003
-1.895
14
.079
-27.0000
14.24781
-57.55851
3.55851
Equal variances not assumed
-1.895
7.177
.099
-27.0000
14.24781
-60.52295
6.52295
Females spent significantly longer using email than males,
t(7.18) = -1.90, p < .05.
Females spent significantly longer using email than males,
t(14) = -1.90, p < .05.
Females and males did not significantly differ in the time spent using email,
t(7.18) = -1.88, ns.
Females and males did not significantly differ in the time spent using email,
t(14) = -1.88, ns.
A researcher was interested in the effects of emotion-evoking music on exam performance. Before their SPSS exam, a lecturer took one group of students to a room in which calming music was being played. A different group of students were taken to another room in which the ‘death march’ was being played. The students then did the exam and their marks were noted. The SPSS output is below. The experimenter made no predictions about which form of support would produce the best exam performance. What should he report?
Group Statistics
Emotional Support
N
Mean
Std.
Deviation
Std. Error Mean
SPSS Exam Mark Positive Support
Negative Support
20
20
65.1500
57.8000
5.0396
15.2129
1.1269
3.4017
Independent Samples Test
Levene’s Test for Equality of Variances
t-test for Equality of Means
F
Sig.
t
df
Sig. (2-tailed)
Mean Difference
Std. Error Difference
95% Confidence
Interval of the Difference
Lower
Upper
SPSS Exam Mark Equal variances
assumed
18.117
.000
2.051
38
.047
7.3500
3.5835
9.559E-02
14.6044
Equal variances not assumed
2.051
23.121
.052
7.3500
3.5835
-6.09E-02
14.7609
Students receiving positive music before the exam did significantly better than those receiving negative music, t(38) = 2.05, p < .05.
Marks for students receiving positive music before the exam did not significantly differ from students receiving negative music, t(38) = 2.05, ns.
Students receiving positive music before the exam did significantly better than those receiving negative music, t(23.12) = 2.05, p < .05, 1-tailed.
Marks for students receiving positive music before the exam did not significantly differ from students receiving negative music, t(23.12) = 2.05, ns.
What does the error bar on an error bar chart represent?
The confidence interval round the mean.
The standard error of the mean.
The standard deviation of the mean.
It can represent any of a, b or c.
The t-test tests for:
Differences between means.
Whether a correlation is significant.
Whether a regression coefficient is equal to zero.
All of the above.
Chapter 8 – Comparing several means
Based on the ANOVA table below calculate the value of F.
ANOVA
SPAIDIF
Sum of Squares
df
Mean Square
F
Between Groups
1582.858
2
791.429
?????
Within Groups
2142.488
45
?????
Total
3725.347
47
a. 0.74
b. 16.62.
c. 4.71.
d. 2.71.
A researcher wanted to see the effects of different learning strategies. A control group simply read the book Discovering statistics (book), a second group read the book and completed the ‘end of chapter exercises’ (book & exercises), and a third group read the book, did the end of chapter examples and also completed the web materials (all activities). The researcher predicted that all activities and book and exercises would perform better than the book group on a subsequent test, but the book and exercises would be worse than the all activities. Which coding scheme would test these hypotheses in a set of planned comparisons?
Case Summariesa
Contrast
Book
Book & Exercises
All Activities
1
2
Contrast 1
Contrast 2
0
0
1
1
1
-1
Limited to first 100 cases.
Case Summariesa
Contrast
Book
Book & Exercises
All Activities
1
2
Contrast 1
Contrast 2
-2
0
1
1
1
-1
a. Limited to first 100 cases.
Case Summariesa
Contrast
Book
Book & Exercises
All Activities
1
2
Contrast 1
Contrast 2
2
0
1
1
1
1
a. Limited to first 100 cases.
Case Summariesa
Contrast
Book
Book & Exercises
All Activities
1
2
Contrast 1
Contrast 2
2
0
-1
-1
-1
-1
a. Limited to first 100 cases.
When variances across groups are unequal, which of the following is not an appropriate course of action.
Use Welch’s F-ratio.
Use Games-Howell post-hoc tests.
Transform the data.
Use Friedman’s ANOVA.
A Bonferroni correction is when.
You apply a criterion for significance based on the usual criterion for significance (0.05) divided by the number of tests performed.
You divide the F-ratio by the number of tests performed.
The degrees of freedom are corrected to make the F-ratio less significant.
The error in the model is adjusted for the number of tests performed.
Levene’s test tests whether:
Data are normally-distributed.
The variances in different groups are equal.
The assumption of sphericity has been met.
Group means differ.
A psychologist was looking at the effects of an intervention on depression levels. Three groups were used: waiting list control, treatment and post treatment (a group who had had the treatment 6 months before). The change in depression levels over the time of the treatment were recorded (although bear in mind only the treatment group actually got any treatment during this time). The SPSS output is below; based on this output what should the researcher conclude:
Test of Homogeneity of Variances
BDIDIF
Levene Statistic
df1
df2
Sig.
4.246
2
45
.020
ANOVA
BDIDIF
Sum of Squares
df
Mean Square
F
Sig.
Between Groups
529.437
2
264.719
5.110
.010
Within Groups
2331.135
45
51.803
Total
2860.572
47
Robust Tests of Equality of Means
BDIDIF
Statistica
df1
df2
Sig.
Welch
Brown-Forsythe
4.345
5.110
2
2
26.436
35.104
.023
.011
Asymptotically F distributed.
The treatment groups did not have a significant effect on the change in depression levels, F(2, 26.44) = 4.35.
The treatment groups had a significantly effect on the change in depression levels, F(2, 35.10) = 5.11.
The treatment groups had a significantly effect on the change in depression levels, F(2, 45) = 5.11.
Chapter 9 – Analysis of Covariance
What assumption does ANCOVA have that ANOVA does not?
Homogeneity of variance.
Homogeneity of regression slopes.
Homoscedasticity.
Homogeneity of sample size.
A music teacher had noticed that some students went to pieces during exams. He wanted to test whether this performance anxiety was different for people playing different instruments. He took groups of guitarists, drummers and pianists (variable = ‘Instru’) and measured their anxiety (Variable = ‘Anxiety’) during the exam. He also noted the type of exam they were performing (in the UK, musical instrument exams are known as ‘grades’ and range from 1 to 8). He wanted to see whether the type of instrument played affected performance anxiety when controlling for the grade of the exam, what analysis should he use?
Analysis of Covariance.
Independent Analysis of Variance.
Repeated Measures Analysis of Variance.
Mixed Analysis of Variance.
The first part of the SPSS output for the example above is below. What does this part of the output tell us?
Levene’s Test of Equality of Error Variancesa
Dependent Variable: ANXIETY
F
df1
df2
Sig.
1.534
2
57
.224
Tests the null hypothesis that the error variance of the dependent variable is equal across groups.
Design: Intercept+GRADE+INSTRU
The type of instrument played did not have a significant effect on anxiety.
The grade of exam taken did not have a significant effect on anxiety.
The variances of anxiety scores were roughly the same in the different groups of musicians.
The variances of anxiety scores were different in the different groups of musicians.
The second part of the SPSS output for the example in the previous 2 questions is below. Which of the following statements best reflects what the effect of ‘INSTRU’ in the table tells us?
Tests of Between-Subjects Effects
Dependent Variable: ANXIETY
Source
Type III Sum of Squares
df
Mean Square
F
Sig.
Corrected Model
8151.482a
3
2717.161
16.317
.000
Intercept
32903.788
1
32903.788
197.594
.000
GRADE
907.833
1
907.833
5.452
.023
INSTRU
6351.708
2
3175.854
19.072
.000
Error
9325.228
56
166.522
Total
465610.477
60
Corrected Total
17476.710
59
R Squared = .466 (Adjusted R Squared = .438)
The type of Instrument played in the exam had a significant effect on the level of anxiety experienced.
The type of Instrument played in the exam did not have a significant effect on the level of anxiety experienced.
The type of Instrument played in the exam had a significant effect on the level of anxiety experienced even after the effect of the grade of the exam had been accounted for.
The type of Instrument played in the exam did not have a significant effect on the level of anxiety experienced even after the effect of the grade of the exam had been accounted for.
Using the SPSS output in the previous question, which of the following statements best reflects what the effect of ‘’GRADE’ in the table tells us?
The grade of exam had a significant relationship with the level of anxiety experienced.
The grade of exam did not have a significant relationship with the level of anxiety experienced.
The type of instrument played had a significant relationship with the grade of exam that was being taken.
The type of instrument played did not have a significant relationship with the grade of exam that was being taken.
The SPSS output below shows the final tables for the example used in the previous 4 questions. Which of the following statements best reflects what these tables tells us?
Estimates
Dependent Variable: ANXIETY
INSTRU
Mean
Std. Error
95% Confidence Interval
Lower Bound
Upper Bound
Guitar
72.633a
3.066
66.490
78.775
Piano
85.852a
2.887
80.068
91.635
Drums
98.225a
2.761
92.694
103.756
a. Covariates appearing in the model are evaluated at the following values: GRADE = 4.5167.
Pairwise Comparisons
Dependent Variable: ANXIETY
(I) INSTRU
(J) INSTRU
Mean Difference
(I-J)
Std. Error
Sig.a
95% Confidence Interval for Differencea
Lower Bound
Upper Bound
Guitar
Piano
-13.219
4.220
.008
-23.634
-2.804
Drums
-25.592
4.148
.000
-35.830
-15.355
Piano
Guitar
13.219
4.220
.008
2.804
23.634
Drums
-12.373
3.989
.009
-22.219
-2.527
Drums
Guitar
25.592
4.148
.000
15.355
35.830
Piano
12.373
3.989
.009
2.527
22.219
Based on estimated marginal means
. The mean difference is significant at the .05 level.
Adjustment for multiple comparisons: Bonferroni.
Guitarists were significantly less anxious than Drummers, but were about as anxious as Pianists, and Drummers were about as anxious as pianists.
Guitarists were significantly less anxious than Pianists and Drummers, and Drummers were significantly less anxious than pianists.
Guitarists, Drummers and Pianists were all about equally anxious.
Guitarists were significantly less anxious than Pianists and Drummers, and Drummers were significantly more anxious than pianists.
Chapter 10 – Factorial ANOVA
How many dependent variables does a two-way ANOVA have?
One
Two
Three.
Four.
An experiment was done to look at the positive arousing effects of imagery on different people. A sample of statistics lecturers was compared against a group of students. Both groups received presentations of positive images (e.g. cats and bunnies), neutral images (e.g. duvets and lightbulbs), and negative images (e.g. corpses and vivisection photographs). Positive arousal was measured physiologically (high values indicate positive arousal) both before and after each batch of images. The order in which participants saw the batches of positive, neutral and negative images was randomised to avoid order effects. It was hypothesised that positive images would increase positive arousal, negative images would reduce positive arousal and that neutral images would have no effect. Differences between the subject groups (lecturers and students) were not expected. What technique should be used to analyse these data?
Two-Way Mixed ANOVA.
Three-Way Repeated Measures ANOVA.
Two-Way Mixed Analysis of Covariance.
Three-way Mixed ANOVA.
In a factorial design, with two factors, if the effect of one factor appears to depend on the levels of the second facto, this is called
A main effect
An interaction effect
A factorial effect
An error
Which of the following is NOT a question answered by two-way anovas?
Does one of other of the factor systematically affect the results?
Are the mean responses the same across all levels of a factor?
Do the two factors interact?
Does one level effect the DV significantly more than the others?
Consider this graph. What is shown in the graph?
Effect of receipt and expectation of alcohol on aggression
12
10
8
6
Expectation yes
Expectation no
4
2
0
yes
no
Receipt
There is an interaction and no main effects
There is one main effect and no interaction
There are two main effects and no interaction
There is an interaction and two main effects
Consider this graph. What is shown in the graph?
Effect of alcohol and expectation on aggresion
12
10
8
6
Expectation yes
Expectation no
4
2
0
yes
no
Receipt
There is an interaction and no main effects
There is one main effect and no interaction
There are two main effects and no interaction
There is an interaction and two main effects
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