Kin 175 Formulas
Point Biserial Correlation:
rpb =
X1 − X0
P1 (P0 )
Sx(avg)
rpb = point biserial correlation
X1 = mean for group 1
X0 = mean for group 0
Sx(avg) = Average of the two standard deviations from group 1 and group 0
P1 = proportion of the people who are in group 1
P0 = proportion of the people who are in group 0
Prediction (predicting Y from X)
^
y = rxy (
Sy
Sx
)(x − X) + Y
ŷ = predicted value of y
rxy = correlation (PPMC) between x and y
x = raw score for x
X = mean of x values
Y = mean of y values
Sx = standard deviation of the x values
Sy = standard deviation of the y values
Standard Error of Estimate
SEE = Sy 1 − rxy2
Sy = standard deviation of the y values
rxy2 = correlation (PPMC) between x and y squared
Standard Error of Measurement
SEM = Sx 1 − R
Sx = standard deviation of the x values
R = reliability (alpha) coefficient
Spearman Brown Prophecy Formula
Rsb =
m(R)
1 + [(m − 1)(R)]
m = the amount you want to boost or diminish test length: new length divided by old/original
length.
R = reliability of the old/original length test
Proportion of Agreement
Pag = Pa + Pd
Pag = proportion of agreement
Pa = proportion of people in cell a
Pd = proportion of people in cell d
Kappa
k=
Pag − Pc
1 − Pc
k = kappa
Pag = proportion of agreement
Pc = proportion of agreement related to chance
Pc = (
a+b a+c
c+d b+d
)(
)+(
)(
)
N
N
N
N
Difficulty Index
nc
N
nc = number of people getting an item correct
N = total number of people in the group
Discrimination Index (Scores)
D p = pt − pb
D p = Difference in proportions
pt = proportion of top group selecting a foil/option
pb = proportion of bottom group selecting a foil/option
Discrimination Index (Classifications)
D p = pm − pnm
pm = proportion of masters selecting a foil/option
pnm = proportion of non-masters selecting a foil/option
Recovery Heart Rate (step test score)
StepScore =
exHR − HR1min postex
10
exHR = exercise heart rate
HR1min postex = heart rate 1 minute after cessation of exercise
Brozek formula:
%bf = [
4.57
− 4.142](100)
bodydensity
%bf = Percent Body Fat
Sloan Prediction Equation (for predicting body density from skinfolds) for men
Yˆ = 1.1043 - .0013(X1 ) - .0013(X 2 )
Yˆ = predicted body density
X1 = thigh skinfold thickness
X2 = scapula skinfold thickness
Sloan Prediction Equation (for predicting body density from skinfolds) for women
Yˆ = 1.0764 - .0008(X1 ) - .0007(X 2 )
X1 = suprailiac skinfold thickness
X2 = tricep skinfold thickness
Body Mass Index
BMI adult =
weight(lb)
(703)
Height(inches)2
Generic Transformation Formula
newscore = Snew (
xold − Xold
) + Xnew
Sold
Snew = Standard deviation of scores on the new scale
Xnew = Mean of scores on the new scale
Sold = Standard deviation of scores on the old/original scale
Xold = Mean of scores on the old/original scale
xold = old/original score
Transformation formula (x to z)
z=
x−X
Sx
z = z score
x = raw score
X = mean of x values
Sx = standard deviation of the x values
Transformation formula (z to x)
x = Sx (z) + X
x = raw score
z = z score
X = mean of x values
Sx = standard deviation of the x values
Curving Scores
CurvedScore = Sxnew (
Xoriginal − Xoriginal
Sxoriginal
) + X xnew
Snew = Standard deviation of scores on the new curved scale
Xnew = Mean of scores on the new curved scale
Sold = Standard deviation of scores on the old/original scale
Xold = Mean of scores on the old/original scale
xold = old/original score