Statistics in APA
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Basic symbols in Statistics
Mean
M = _____ or
=
 = ________
M = is being promoted by the

APA but = is still widely in
use especially internationally
 = indicates a population mean

Standard
Deviation
SD = _____
 = ______
Measures of Effect Size
Cohen’s d
d = _____.
Correlation
r(df) = _____
Effect size for
Anova
Eta-Squared
Confidence Intervals
CI for a Mean or for a mean
of difference
Significance Tests
One Sample t
Test Independent
Samples t Test
Matched Samples
t Test
One-Way
ANOVA
Two-Way ANOVA
Chi Square Goodness-of-Fit
η2 = _____.
M = or
indicates sample
mean
SD = _____ indicates a sample
standard deviation
 = ______ indicates a
population standard deviation
This is followed or preceded by a
statement of the small, medium
or large
____% CI [ ___, ___ ]
t(df) = ____, p = ____.
F(df1,df2) = ___, p = ___.
2(df, N=
)= ____, p = ____
.
Means and Standard Deviations
Mean and Standard Deviation are most clearly presented in
parentheses:
The sample as a whole was relatively young (M = 19.22, SD =
3.45).
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The average age of students was 19.22 years (SD = 3.45).
Percentages
Percentages are easiest to read when presented
with no decimal places.
in parentheses
Over half the sample (58%) could not correctly identify in which
state Washington D.C. was located.
Tables
You are trying to present data is the easiest form to read
without loosing its meaning.
For example Several means and standard deviations may beeasier
to read when displayed in a table. Tables are useful if you find
that a paragraph has almost as many numbers as words.
Group
Control group
Practice only
group
Instruction
only group
Practice and
Instruction
group
Mean
23
27
SD
1.3
1.1
28
1.4
32
1.2
Tables have no vertical lines and horizontal lines only at the
beginning and end.
Tables are identified with arabic numerals sequentially. Ie.
Your first table is Table 1 and the next is Table 2 etc.
Do not use both a sentence and a table, choose one or the other.
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How to Report
Z-tests results
As the results are not significantly different z(100)=-1.875, p>.05 there is
no reason to assume that the sample scores are significantly different form
the general population.
T tests
“A significant difference (p<.02) was found between male’s and female’s scores on the
Masterson Word Association Test with males making more negative associations than
females. t(98)=2.4, p <.02” A d of .95 indicated a strong effect.
There is a significance between the anxiety levels of this most recent sample and
previous samples t(11) = -2.56, p < .03. The most recent sample had a lower anxiety
level (M = 5.69) compared to the earlier samples (M= 11.5)
The traditional southern states have an infant mortality rate (M = 8.3) significantly
higher than the n
Notw the z and the t and the p are either italicized z, t, p or underlined z, t, p. This is
true of all statistical symbols
Two sample T
The sample was significantly different form the national average of 6.7 t (10), p <.002.
The effect size was strong d = 1.25.
The results found that the male mean(M= .53, S = .0070) interest in
violence was significantly greater than the female mean (M = .50, S
= .0084) interest in violence, t(98) = 2.4, p < .02. The magnitude of the
difference in means was moderate. (d = .50)”
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Pared sample t-tests
The difference between the first and the second games was significant ( t(26)
=2.4, p <.03) with the mean of group one being 211.2 and the mean of Group
being 195.59. d = 1.2. Also the comparisons between the first and third game
resulted in a difference significant at the p = >.6 level There was clearly no
significant difference between the mean for the second game and third game
t(26)=--.665, P >.05
Correlations
There is a good negative correlations between median income and percent
unemployed. r = -.56, p<.01. In other words as unemployment goes up median family
income goes down
One Way Anova
An analysis of variance showed that the effect of a curfew on grades was significant,
F(3,27) = 5.94, p = .007. Post hoc analyses was conducted using a Tukey HSD and
a.05 level of significance was achieved with the 9:00 group having a higher GPA ( M =
3.21, SD .56 than in the 11:00 ( M = 2.85 SD = .72) and the no curfew group ( M = 2.6.
S.D 1.2)
A one way ANOVA showed that the difference in quiz scores between the control
group (N = 3, M = 4.000, SD = 1.000), the first experimental group (N = 3, M = 8.000,
SD = 1.000), and the second experimental group (N = 3, M = 9.000, SD =1.000) were
statistically significant, F(2,6) = 21.000, p = .002, η2 = .875. Tukey’s HSD tests showed
that both experimental groups scored statistically significantly higher than the control
group. However, the two experimental groups did not differ significantly.
A two way ANOVA
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A therapist was interested in determining the effects of Prozac and insight
therapy on gambling habits of compulsive gamblers.
40 participants were randomly assigned to each level of a 2 main One main
effect being Medication (Prozac)(with two levels 10mg and 40mg)and the other
Insight therapy (with two levels 1 hour per week and 5 hours per week).
In one condition the participant received 1 hour per week of insight therapy and
10 mg of Prozac
A second group received 5
hours of insight therapy per week and 20 mg of Prozac.
Another received 40 mg of Prozac and 1 hour of insight therapy
and the final group received 5 hours of insight therapy and 40 mg of Prozac. At
the end of six months the amount of gambling determined by the amount of
bets placed was measured.
The relevant SPSS output is shown below.
There is a main effect of the Insight therapy.
The level therapy does have an effect on amount of gambling, F(l, 36) = 101.721,
p = .000. More specifically, those who received 5 hours of insight therapy per
week gambled significantly less than those who only received 1 hour per week.
(M = $58.00 versus M = $ 235).
Usually source table are included
Tests of Between-Subjects Effects
Dependent Variable: perceived warmth
Source
Corrected
Model
Intercept
Medication
Therapy
Med *
Therapy
Error
Total
Type III Sum
of Squares
103.905*
df
5
Mean
Square
20.781
F
30.447
1761.524
31.476
69.429
1
2
1
1761.524
15.738
69.429
2580.837
23.058
101.721
.000
.000
.000
.000
3.000
2
1.500
2.198
.126
24.571
1890.000
36
42
.683
Sig
Statistics in APA
Corrected
Total
6
128.476
41
3. R Squared = .809 (Adjusted R Squared = .782)
A Two Way Anova with no interactions
In addition increased medication also had a main
effect on reducing gambling F(1,36) = 23.05, p = .000.
There was no interaction F(2,36) = 2.198, P >.05
Chi Square
Chi-Square statistics are reported with degrees of freedom and sample size in
parentheses, the Pearson chi-square value (rounded to two decimal places), and the
significance level:
The percentage of participants that were married did not differ by gender, 2(1, N = 90)
= 0.89, p = .35.
Of the 87 abused spouses in the study 27 had called the police at least once, 30 had
left the situation and 30 had remained in the situation without seeking help. These
frequencies were significantly different, 2 (3, N = 87) = 9.1, p < .03.