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Formula Sheet
Proportion: P = f / N; where f is the frequency and N is the total number of cases
Percent: % = (f / N) * 100
To find the middle case (for the median):
The mean of Y: Y 
Y
N
N 1
2
; Where Y is a case’s score on the variable Y and N is the total number of cases.
Range=Maximum-minimum
Inter-quartile Range:
N * .75;
The variance of Y and X: S
2
Y
N * .25
 (Y  Y )

IQR=UQ-LQ
2
S
N 1
The standard deviation of Y and X: SY 
(Y  Y )
2
X
( X  X )

2
N 1
2
SX 
N 1
( X  X )
2
N 1
Z score: Z  Y  Y ; where Y is a raw score, Y is the mean of Y , and SY is the standard deviation of Y
SY
Raw score: Y  Y  ( Z * S Y ) ; where Z is a z score (a.k.a. standard score)
Confidence interval for a mean: CI  Y  ( Z * SY ) ; where S Y is the standard error of the mean
Standard error of the mean: S 
Y
SY
N
; where SY is the standard deviation of Y and N is the number of cases in the
sample
Confidence interval for a proportion: CI  p  ( Z * S p )
Confidence interval for a percentage: CI  %  ( Z * S % )
Standard error of the proportion: S p  ( p)(1  p)
N
Standard error of the percentage: S %  (%)(100  %)
N
95% → Z=1.96
99% → Z=2.58
1
Observed t value for a difference in means test: t 
Y 1 Y 2
; where Y 1 is the mean for group 1, Y 2 is the mean for
S Y 1 Y 2
group 2, and SY 1 Y 2 is the standard error for the difference in means
Standard error for the difference in means (when population variances are assumed equal):
S Y 1 Y 2 
( N 1  1) S Y21  ( N 2  1) S Y22
( N1  N 2 )  2
sample for group 2,
S
2
Y1
N1  N 2
; where N1 is the size of the sample for group 1, N2 is the size of the
N1 N 2
is the variance for group 1, and
S
2
Y2
is the variance for group 2
Degrees of freedom for a difference in means test: df = (N1 + N2) – 2
Observed z value for the difference in proportions test: Z  p1  p 2 ; where p1 and p2 are the sample proportions for
S p1  p2
groups 1 and 2
The standard error for the difference in proportions test: S p  p 
1
2
Chi-squared:  2 
p1 (1  p1 ) p 2 (1  p 2 )

N1
N2
( fo  fe )2
; where fo is the observed frequencies in each cell and fe is the expected frequencies (if
 f
e
the two variables are statistically independent)
fe 
ColumnM arg inal * RowM arg inal
N
Degrees of freedom for chi-squared: df=(r-1)(c-1); where r is the number of rows and c is the number of columns
Lambda=
E1  E 2
; Where E1 is the number of prediction errors made when the independent variable is ignored and E2 is
E1
the number of predictions errors made when the independent variable is not ignored.


A regression equation: Y  a  bX ; where Y is the predicted score on Y given a, b, and X
The regression slope: b 
SYX
S X2
The y-intercept: a  Y  (b * X )
Degrees of freedom (for hypothesis tests about the slope): df=n-2; where n is the number of cases in the data
The covariance between Y and X: SYX 
Pearson’s correlation coefficient: r 
 ( X  X )(Y  Y )
N 1
SYX
SY * S X
The coefficient of determination (a.k.a. r-squared): r 2  r * r
2