Guide to Statistical Techniques
Commonly Used in the Social Sciences
Correlation:
Compare two variables that are both continuous
Multiple regression:
Use several continuous variables to predict another continuous variable
Z-test:
Compare an individual score or sample mean to an overall population mean, when the population
mean and standard deviation are known
Single-sample t-test:
Compare a sample mean to the overall population mean, when the population mean is known but
the population standard deviation in unknown (sample standard deviation used instead)
Between-group t-test:
Compare two groups (samples) of people along some continuous variable; used in most cases
when a two-category variable is compared to a continuous variable
Repeated-measures (within-subject) t-test:
Compare the same group of people across two time points along some continuous variable; also
sometimes used with matched samples
ANOVA:
Used to compare multiple groups of people along some continuous variable; used in most cases
when a multi-category variable is compared to a continuous variable
Repeated-measures ANOVA:
Used to compare the same group of people across multiple time points on some categorical
variable
Post-hoc test:
Clarifies a significant result by demonstrating which of several groups differ from each other
Chi-square test for goodness of fit:
Used to determine whether the observed percentages of people within various categories are
reliably different from those hypothesized or expected; usually involves a single categorical
variable
Chi-square test for independence:
Used to determine if one categorical variable is related to another categorical variable; usually
used when analyses involve two or more categorical variables
Correlations:
impossible!
large
medium
small
zero / near-zero
small
medium
large
impossible!
more extreme than +1.00
+.50 to +1.00
+.30 to +.49
+.10 to +.29
0 ish
-.10 to -.29
-.30 to -.49
-.50 to -1.00
more extreme than -1.00
positive
(direct)
negative
(inverse)
Cohen’s d:
large
medium
small
zero / near-zero
small
medium
large
+.80 to infinity
+.50 to +.79
+.20 to +.49
0 ish
-.20 to -.49
-.50 to -.79
-.80 to -infinity
Z/T/IQ:
T scores 20
IQ scores 55
30
70
40
85
50
100
60
115
70
130
80
145
increase
(higher)
decrease
(lower)
Unit 1: Introductory Statistics
13
Which of the following correlation coefficients represents a correlation of the greatest
magnitude?
a) r = -0.43 38%, r =.69
b) r = +0.37
c) r = +1.26
15
Which of the following likely represents the correlation between anxiety and
happiness?
a) r = -0.51 68%, r =.23
b) r = +0.23
c) r = -2.36
21
If I announced that I would give an “A” in the course to anyone who brings me a
peanut butter sandwich a la mode, what should you bring me?
a) a peanut butter sandwich with ice cream on the side
b) a peanut butter sandwich and a calculator
c) a peanut butter and jelly sandwich 72%, r =.62
23
In general, what type of grade distribution would students prefer for their course
grades?
a) positive skew
b) negative skew 68%, r =.15
c) symmetrical
25
A researcher designs a study, where participants are asked to rate their level of anxiety
on a scale from 1 (no anxiety) to 9 (high anxiety. In this study, “anxiety” would best
be described as what type of variable?
a) polygamous
b) continuous 80%, r =.31
c) categorical
Unit 2: Correlation and Regression
4
Magnitude of the correlation for r = .27
a) small (88%, r = .23)
b) medium
c) large
12
If 5 points are added on to each student’s test score, what would happen to the standard
deviation?
a) stay the same (82%, r = .31)
b) get 5 points higher
c) get 5 times bigger
15
Using SPSS, you find that happiness correlates r = -.20 with physical health. This
means that _____ percent of the differences in health can be explained by happiness.
a) 2
b) 4 (55%, r = .85)
c) 20
20
Lowest possible value for R:
a) negative infinity
b) -1
c) 0 (39%, r = .39)
23
Psychological tests and medical tests are both used to predict important outcomes.
Psychological tests usually yield correlations with relevant outcomes that are _______
those of medical test.
a) much stronger than
b) similar to (71%, r = .69)
c) much weaker than
Unit 3: Standard Scores
2
Which of the following scores is closest to the mean?
a) T = 39
74%, r = .46
b) IQ = 114
c) Z = 1.16
8
Range of Z scores:
70%, r = .54
a) -∞ to ∞
b) -1 to 1
c) -4 to 4
13
Discrepancy between a sample statistic and a population parameter:
72%, r = .69
a) Sampling error
b) Z score
c) Standard error of the mean
18
After college, you spend a couple years working in a hospital, and all incoming
patients are required to fill out a short personality survey. You notice the “pain”
and “self-efficacy” scores for three patients. Of the following three patients who
will likely be easiest to treat?
a) Client A. Pain: T = 31. Self-efficacy: Z = -1.36
80%, r = .46
b) Client B. Pain: T = 36. Self-efficacy: Z = 0.57
c) Client C. Pain: T = 72. Self-efficacy: Z = 0.69
22
When it comes to hypothesis testing, the “p-value” describes…
a) the probability that the resulting statistic was obtained by chance 80%, r = .46
b) the probability that the resulting statistic is correct or true
c) the probability that the result will generalize to the population
Unit 4: Z- and t- tests
5
A null hypothesis states describes that there are no differences expected to
occur at this level:
a) measurement
b) sample
c) population -- 73%, r = .18
9
The results of a multiple regression indicate that R2 = .20, p = .50. Is this result
statistically significant?
a) non-significant -- 78%, r = .27
b) significant
c) not enough information
13
Assume that the alternative hypothesis is accurate. If the researcher finds no
effect, what has occurred?
a) Type I error
b) Type II error -- 87%, r = .18
c) Iatrogenic error
14
Effect size for Cohen’s d = .36
a) small -- 82%, r = .36
b) medium
c) large
15
You have people rate how much they enjoy Coke and how much they enjoy
Pepsi. The mean enjoyment rating for Coke is a bit higher than for Pepsi, and
you find d = 1.25, t = 1.67, p = .63. How would you most likely get a result like
this?
a) large effect but a small sample -- 73%, r = .46
b) unusual sample
c) poor methodology or survey items
Unit 5: ANOVA and Chi-square
6
Using ANOVA, F will always fall within what range?
a) between negative infinity and infinity
b) between 0 and 1
c) between 0 and infinity  correct
10
Statistical test most appropriate for comparing depression (diagnosis vs. no
diagnosis) to favorite color (blue vs. black vs. other)
a) correlation (r)
b) ANOVA (F)
c) chi-square (χ2)  correct
15
Which of the following most represents a significant ANOVA correctly typed in
APA format?
a) The ANOVA was statistically significant, F(3, 256) = 12.31, p > .05
b) The ANOVA was statistically significant, F(5, 61) = 1.13, p < .001
c) The ANOVA was statistically significant, F(4, 81) = 7.13, p = .04  correct
18
As variability due to chance decreases, the value of F will
a) increase  correct
b) stay the same
c) decrease
23
Type of test typically used for longitudinal studies
a) ANOVA
b) repeated-measures ANOVA  correct
c) chi-square test for goodness of fit
SPSS Output
Correlations
68. Depres sion
69. Lis ten to Loud Music
70. Parents Fought
Growing Up
91. Object Relations
97. Attractivenes s
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
68.
Depres sion
1
279
.096
.109
279
.238**
.000
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
69. Lis ten to
Loud Music
.096
.109
279
1
279
.105
.080
70. Parents
Fought
91. Object
97.
Growing Up
Relations
Attractiveness
.238**
-.168**
-.328**
.000
.005
.000
279
279
279
.105
-.069
.057
.080
.253
.346
279
279
279
1
-.104
-.086
.082
.152
279
279
279
279
279
-.168**
.005
279
-.328**
.000
279
-.069
.253
279
.057
.346
279
-.104
.082
279
-.086
.152
279
1
.104
.084
279
1
279
.104
.084
279
279
**. Correlation is s ignificant at the 0.01 level (2-tailed).
Correl ations
83. Self-Es teem
59. Worrying
90. Political Idealis m
97. Att ract iveness
104. Neuroticis m
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
Pearson Correlation
Sig. (2-tailed)
N
83.
Self-Es teem
1
59. Worrying
-.316**
.000
279
279
-.316**
1
.000
279
279
-.042
.109
.486
.069
279
279
.413**
-.212**
.000
.000
279
279
-.472**
.653**
.000
.000
279
279
**. Correlation is s ignificant at the 0.01 level (2-tailed).
*. Correlation is s ignificant at the 0.05 level (2-tailed).
90. Political
Idealis m
-.042
.486
279
.109
.069
279
1
97.
104.
At tract iveness Neurot icism
.413**
-.472**
.000
.000
279
279
-.212**
.653**
.000
.000
279
279
-.075
.128*
.212
.033
279
279
279
-.075
1
-.221**
.212
.000
279
279
279
.128*
-.221**
1
.033
.000
279
279
279
Model Summary
Model
1
R
.237a
R Square
.056
Adjusted
R Square
.046
Std. Error of
the Estimate
1.097
a. Predictors: (Constant), 96. Anger, 44. Age, 79.
Pro-Environment
ANOVAb
Model
1
Regres sion
Residual
Total
Sum of
Squares
19.764
330.673
350.437
df
Mean Square
6.588
1.202
3
275
278
F
5.479
Sig.
.001a
a. Predic tors: (Constant), 96. Anger, 44. Age, 79. Pro-Environment
b. Dependent Variable: 62. Stealing
Group Sta tisti cs
37. Days per W eek
Eating Breakfast
107. Consc ient ious ness
16. Relationship St atus
Single
In a Relationship
Single
In a Relationship
N
113
166
113
166
Mean
3.27
3.99
6.04
6.42
St d. Deviat ion
2.281
2.466
1.861
1.749
St d. Error
Mean
.215
.191
.175
.136
Independent Samples Test
Levene's Test for
Equality of Variances
F
37. Days per Week
Eating Breakfas t
107. Conscientiousness
Equal variances
as sumed
Equal variances
not ass umed
Equal variances
as sumed
Equal variances
not ass umed
1.919
.325
Sig.
.167
.569
t-test for Equality of Means
t
df
Sig. (2-tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
-2.466
277
.014
-.720
.292
-1.294
-.145
-2.503
252.586
.013
-.720
.287
-1.286
-.153
-1.765
277
.079
-.386
.219
-.817
.045
-1.744
230.552
.083
-.386
.222
-.823
.050
Group Sta tisti cs
57. Cell Phone Use
49. Smoking
21. Socioeconomic
St atus (SES)
Lower-Middle Class
Upper-Middle Class
Lower-Middle Class
Upper-Middle Class
N
121
135
121
135
Mean
6.84
7.08
3.00
1.99
St d. Deviat ion
2.025
1.697
2.890
2.086
St d. Error
Mean
.184
.146
.263
.180
Independent Samples Test
Levene's Test for
Equality of Variances
F
57. Cell Phone Use
49. Smoking
Equal variances
as sumed
Equal variances
not ass umed
Equal variances
as sumed
Equal variances
not ass umed
1.591
25.326
Sig.
.208
.000
t-test for Equality of Means
t
df
Sig. (2-tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
-1.025
254
.306
-.239
.233
-.697
.220
-1.015
235.210
.311
-.239
.235
-.701
.224
3.221
254
.001
1.007
.313
.392
1.623
3.166
216.055
.002
1.007
.318
.380
1.635
De scri ptives
92. Life Satisfaction
N
TV
Int ernet
Books
Ex ercise
Total
Mean
6.20
6.55
6.87
7.17
6.57
93
87
75
24
279
St d.
Deviation
1.857
1.903
1.436
1.308
1.747
St d. Error
.193
.204
.166
.267
.105
95% Confidenc e
Int erval for Mean
Lower
Upper
Bound
Bound
5.82
6.59
6.15
6.96
6.54
7.20
6.61
7.72
6.37
6.78
Minimum
1
1
3
4
1
Maximum
9
9
9
9
9
ANOVA
92. Life Satisfaction
Between Groups
W ithin Groups
Total
Sum of
Squares
27.608
820.636
848.244
df
3
275
278
Mean Square
9.203
2.984
F
3.084
Sig.
.028
Post Hoc Tests
Multiple Comparisons
Dependent Variable: 92. Life Satis faction
LSD
(I) 26. Favorite
Entertainment
TV
Internet
Books
Exercis e
(J) 26. Favorite
Entertainment
Internet
Books
Exercis e
TV
Books
Exercis e
TV
Internet
Exercis e
TV
Internet
Books
Mean
Difference
(I-J)
-.347
-.662*
-.962*
.347
-.315
-.615
.662*
.315
-.300
.962*
.615
.300
Std. Error
.258
.268
.396
.258
.272
.398
.268
.272
.405
.396
.398
.405
*. The mean difference is s ignificant at the .05 level.
Sig.
.179
.014
.016
.179
.248
.124
.014
.248
.460
.016
.124
.460
95% Confidence Interval
Lower Bound Upper Bound
-.85
.16
-1.19
-.13
-1.74
-.18
-.16
.85
-.85
.22
-1.40
.17
.13
1.19
-.22
.85
-1.10
.50
.18
1.74
-.17
1.40
-.50
1.10
Descriptive Statistics
Mean
8.0645
6.6452
7.6774
Intake
Discharge
Follow-up
Std. Deviation
1.80620
1.42708
2.11955
N
31
31
31
Tests of Within-Subjects Effects
Measure: MEASURE_1
Source
factor1
Error(factor1)
Sphericity Assumed
Greenhous e-Geisser
Huynh-Feldt
Lower-bound
Sphericity Assumed
Greenhous e-Geisser
Huynh-Feldt
Lower-bound
Type III Sum
of Squares
33.376
33.376
33.376
33.376
237.290
237.290
237.290
237.290
df
2
1.980
2.000
1.000
60
59.388
60.000
30.000
Mean Square
16.688
16.860
16.688
33.376
3.955
3.996
3.955
7.910
F
4.220
4.319
4.319
4.373
Pairwise Comparisons
Measure: MEASURE_1
(I) factor1
1
2
3
(J) factor1
2
3
1
3
1
2
Mean
Difference
(I-J)
1.419*
.387
-1.419*
-1.032
-.387
1.032
Std. Error
.503
.483
.503
.528
.483
.528
a
Sig.
.008
.430
.008
.060
.430
.060
95% Confidence Interval for
a
Difference
Lower Bound Upper Bound
.392
2.447
-.600
1.374
-2.447
-.392
-2.110
.045
-1.374
.600
-.045
2.110
Based on estimated marginal means
*. The mean difference is s ignificant at the .05 level.
a. Adjustment for multiple comparis ons : Least Significant Difference (equivalent to no
adjustments).
Sig.
.019
.020
.019
.049
27. Anima l for a Day * 16. Rel ationship S tatus Crosstabulation
27. Animal
for a Day
Dolphin
Eagle
Horse
Dog
Turtle
Total
Count
Ex pec ted Count
Count
Ex pec ted Count
Count
Ex pec ted Count
Count
Ex pec ted Count
Count
Ex pec ted Count
Count
Ex pec ted Count
16. Relationship St atus
In a
Single
Relationship
41
50
36.9
54.1
42
59
40.9
60.1
9
7
6.5
9.5
16
49
26.3
38.7
5
1
2.4
3.6
113
166
113.0
166.0
Chi-Square Te sts
Pearson Chi-Square
Lik elihood Ratio
Linear-by-Linear
As soc iation
N of Valid Cases
Value
13.854 a
14.359
2.183
4
4
As ymp. Sig.
(2-sided)
.008
.006
1
.140
df
279
a. 2 c ells (20.0%) have ex pec ted c ount les s than 5. The
minimum expected count is 2.43.
Total
91
91.0
101
101.0
16
16.0
65
65.0
6
6.0
279
279.0
2 of 15: Athletics
If halfway through the
season the Detroit
Pistons basketball team
has won 85% of their
games, what will likely be
their win
percentage
at the end of
the year?
6 of 15: Personnel Selection
What’s the correlation
between success in a job
interview and success on
the job?
73%
79%
85%
r = .00
none
r = .20
mild
r = .40
modest
7 of 15: Romance
Using judges’ ratings,
how highly does a
person’s level of
attractiveness correlate
with that of their romantic
partner?
r = .10
weak
r = .40
modest
r = .70
strong
11 of 15: College Recruitment
What’s the correlation
between ACT scores and
college
GPA?
r = .00
none
r = .20
mild
r = .40
modest
14 of 15: Physical Therapy
What’s the correlation
between self-efficacy
scores and successful
physical rehabilitation?
Waterboy,
You can do it!
r = .00
none
r = .30
modest
r = .60
strong
Grades
• Grades in this course will be based largely
on effort. What you put in, you will get out.
• “We maximize choice and enhance power
by deciding for ourselves how much is
good enough in each and every activity we
engage in. We all have the inalienable
right to waste our potential.” –Kaufman
• Recommendations