Heiman G. Basic Statistics for the Behavioral Sciences
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importance of, 110
linear interpretation of, 381–384
sample mean and, 124–128
for transforming sample mean into
z-score, 206
for transforming z-score in population
into raw score, 114
for transforming z-score in sample into
raw score, 113–114
and use of z-table, 120–122
1X
2
468 Index
z-table, 120–122, 419–422
z-test. See also Critical value of ; z
obtained
and computing confidence interval, 245
and computing 236
formula for, 216–217, 233
importance of, 208
inferential statistics and, 208
one-tailed testing and, 223, 229
performing, 215–218
t
obt
,
1z
obt
2
z1z
crit
2
power and, 228-229
summary of, 220
Type I error and, 228
Type II error and, 228
when to perform, 234
See Critical value of z
Zero, as sum of deviations around the mean,
70–71
Zero association, 146
1zcrit2z
crit
.
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Chapter 3
N number of scores in the data
f frequency
cf cumulative frequency
rel. f relative frequency
Chapter 4
X scores
Y scores
K constant
⌺X sum of X
Mdn median
X
苶
sample mean of Xs
X ⫺ X
苶
deviation
mu; population mean
⌺(X ⫺ X
苶
) sum of deviations around the mean
Chapter 5
⌺X
2
sum of squared Xs
(⌺X)
2
squared sum of Xs
S
X
sample standard deviation
S
2
X
sample variance
σ
X
population standard deviation
σ
2
X
population variance
s
X
estimated population standard deviation
s
2
X
estimated population variance
df degrees of freedom
Chapter 6
⫾ plus or minus
zz-score
σ
X
苶
standard error of the mean
Chapter 7
Y
苶
sample mean of Ys
⌺Y sum of Ys
⌺Y
2
sum of squared Ys
(⌺Y)
2
squared sum of Ys
⌺XY sum of cross products of X and Y
D difference score
r Pearson correlation coefficient
r
S
Spearman correlation coefficient
Chapter 8
Y′ Y prime; predicted value of Y
S
2
Y′
variance of the Y scores around Y′
S
Y′
standard error of the estimate
b slope of the regression line
aY-intercept of the regression line
r
2
coefficient of determination
1 ⫺ r
2
coefficient of alienation
Chapter 9
p probability
p(A) probability of event A
Chapter 10
⬎ greater than
⬍ less than
ⱖ greater than or equal to
ⱕ less than or equal to
⫽ not equal to
H
a
alternative hypothesis
H
0
null hypothesis
z
obt
obtained value of z-test
z
crit
critical value of z-test
␣ alpha; theoretical probability of a Type I error
 beta; theoretical probability of a Type II error
1 ⫺ power
List of Symbols
Chapter 11
t
obt
obtained value in t-test
t
crit
critical value of t-test
s
X
苶
estimated standard error of the mean
rho; population correlation coefficient
r
obt
obtained value of r
r
crit
critical value of r
Chapter 12
n number of scores in each sample
s
2
pool
pooled variance
s
X
苶
1
⫺X
苶
2
standard error of the difference
D
苶
mean of difference scores
D
mean of population of difference scores
s
2
D
estimated variance of population of difference
scores
s
D
苶
standard error of the mean difference
r
2
pb
effect size in a two-sample experiment
Chapter 13
ANOVA analysis of variance
k number of levels in a factor
F
obt
obtained value from F-ratio
F
crit
critical value of F
σ
2
error
population error variance
σ
2
treat
population treatment variance
MS
wn
mean square within groups
df
wn
degrees of freedom within groups
SS
wn
sum of squares within groups
MS
bn
mean square between groups
df
bn
degrees of freedom between groups
SS
bn
sum of squares between groups
SS
tot
total sum of squares
df
tot
total degrees of freedom
q
k
value used in HSD test
HSD Tukey’s honestly significant difference
2
eta squared; effect size in the sample
Chapter 14
F
A
obtained F for factor A
F
B
obtained F for factor B
F
A⫻B
obtained F for interaction of A and B
Chapter 15
f
o
observed frequency
f
e
expected frequency
2
obt
obtained value in chi square procedure
2
crit
critical value in chi square procedure
phi coefficient
C contingency coefficient
⌺R sum of ranks
⌺R
exp
expected sum of ranks
U
obt
obtained value in Mann–Whitney U test
T
obt
obtained value in Wilcoxon T test
H
obt
obtained value in Kruskal–Wallis H test
z
obt
obtained value in rank sums test
2
obt
obtained value in Friedman
2
test