2S
1S
N
2
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FREQUENTLY USED FORMULAS
CHAPTER 2
Proportions
Z 1obtained2 Proportion
f
N
CHAPTER 9
Percentage
Means
p
% a
f
b 100
N
Z 1obtained2 CHAPTER 3
Ps Pu
1Pu 11 Pu 2/N
1X1 X2 2
sx x
Mean
Standard deviation of the sampling
distribution for sample means
X sx x g 1Xi 2
N
Pooled estimate of population proportion
CHAPTER 4
Standard deviation
s
g 1Xi X 2 2
N
B
Pu N1Ps1 N2Ps2
N1 N2
Standard deviation of the sampling
distribution for sample proportions
spp 1Pu 11 Pu 2 11N1 N2 2/N1N2
CHAPTER 5
Z scores
Zi s 22
s 21
B N1 1
N2 1
Proportions
Xi X
s
Z 1obtained2 CHAPTER 7
1Ps1 Ps2 2
spp
CHAPTER 10
Confidence interval for a sample mean
Total sum of squares
c.i. X Z a
SST a X 2 NX 2
Sum of squares between
s
b
1N 1
Confidence interval for a sample proportion
c.i. Ps Z
Pu 11 Pu 2
B
N
CHAPTER 8
Sum of squares within
SSW SST SSB
Degrees of freedom for SSW
Means
Z 1obtained2 SSB a Nk 1Xk X 2 2
dfw N k
X m
s/ 1N 1
Degrees of freedom for SSB
dfb k 1
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Mean square within
SSW
dfw
MSW Mean square between
MSB SSB
dfb
Slope
b
1X X 2 1Y Y 2
1X X 2 2
Y intercept
a Y bX
Pearson’s r
1X X 2 1Y Y 2
F ratio
MSB
F
MSW
CHAPTER 11
Chi square
1 fo fe 2 2
x 1obtained2 a
fe
2
CHAPTER 13
Phi
x2
f
BN
Cramer’s V
x2
V
B 1N 2 1Minimum of r 1, c 12
Lambda
CHAPTER 14
Gamma
Ns Nd
Ns Nd
Spearman’s rho
rs 1 231X X 2 2 4 31Y Y 2 2 4
CHAPTER 17
Partial correlation coefficient
ryx.z ryx 1ryz 2 1rxz 2
21 r 2yz 21 r 2xz
Least-squares multiple regression line
Y a b1X1 b2X2
Partial slope for X1
b1 a
sy
s1
ba
ry1 ry2 r12
1 r 212
b
Partial slope for X2
b2 a
sy
s2
ba
ry2 ry1 r12
1 r 212
b
Y intercept
E1 E2
l
E1
G
r
6 g D2
N 1N 2 12
CHAPTER 15
Least-squares regression line
Y a bX
a Y b1X1 b2X2
Beta-weight for X1
b*1 b1 a
s1
b
sy
Beta-weight for X2
b*2 b2 a
s2
b
sy
Standardized least-squares regression line
Zy b*1 Z1 b*2 Z2
Coefficient of multiple determination
R 2 r 2y1 r 2y2.1 11 r 2y1 2
2S
1S
N
3
2S
1S
N
4
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GLOSSARY OF SYMBOLS
The number in parentheses indicates the chapter in which the symbol is introduced.
a
Point at which the regression line
crosses the Y axis (15)
ANOVA
The analysis of variance (10)
b
Slope of the regression line (15)
bi
Partial slope of the linear relationship
between the ith independent variable
and the dependent variable (17)
b*i
Standardized partial slope of the
linear relationship between the ith
independent variable and the
dependent variable (17)
df
Degrees of freedom (8)
f
Frequency (2)
F
The F ratio (10)
fe
Expected frequency (11)
fo
Observed frequency (11)
G
Gamma for a sample (14)
Gp
Partial gamma (16)
H0
Null hypothesis (8)
H1
Research or alternate hypothesis (8)
IQV
Index of qualitative variation (4)
Md
Median (3)
Mo
Mode (3)
N
Number of cases (2)
Nd
Number of pairs of cases ranked in
different order on two variables (14)
Ns
Number of pairs of cases ranked in
the same order on two variables (14)
%
Percentage (2)
P
Proportion (2)
Ps
A sample proportion (7)
Pu
A population proportion (7)
PRE
Proportional reduction in error (13)
Q
Interquartile range (4)
r
Pearson’s correlation coefficient for
a sample (15)
r2
Coefficient of determination (15)
R
Range (4)
rs
Spearman’s rho for a sample (14)
rxy.z
Partial correlation coefficient (17)
R2
Multiple correlation coefficient (17)
s
Sample standard deviation (4)
SSB
The sum of squares between (10)
SST
The total sum of squares (10)
SSW
The sum of squares within (10)
s
2
Sample variance (4)
t
Student’s t score (8)
V
Cramer’s V (13)
X
Any independent variable (12)
X
Mean of a sample (3)
Xi
Any score in a distribution (3)
Y
Any dependent variable (12)
Y
A predicted score on Y (15)
Z scores
Standard scores (5)
Z
A control variable (16)
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GREEK LETTERS
sp
Standard deviation of a sampling
distribution of sample proportions (6)
spp
Standard deviation of the sampling
distribution of difference in sample
proportions (9)
sX
Standard deviation of a sampling
distribution of sample means (6)
s X X
Standard deviation of the sampling
distribution of the difference in
sample means (9)
s2
Population variance (4)
a
Probability of Type I error (8)
b
Probability of Type II error (8)
g
Gamma for a population (14)
l
Lambda (13)
m
Mean of a population (3)
mp
Mean of a sampling distribution of
sample proportions (6)
mX
Mean of a sampling distribution of
sample means (6)
r
Pearson’s correlation coefficient for
a population (15)
g
“Summation of” (3)
f
Phi (13)
Spearman’s rho for a population (14)
x2
Chi square statistic (11)
Population standard deviation (4)
x2c
Chi square corrected by Yates’
correction (11)
rs
s
2S
1S
N
5