Intro to Statistics Formula Sheet - Tyndale University
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Intro to Statistics Formula Sheet
CATEGORY 1 CATEGORY 2 CATEGORY 3
CATEGORY 4 CATEGORY 5 CATEGORY 6
A) Reminder:
BEDM(S)AS ? Brackets, Exponents, Division, Multiplication, Sum ( ), Addition, Subtraction
B) Central Tendency (Ch. 3)
Population mean: ? =
X N
Sample
mean:
M
=
X n
C) Sum of Squares (Ch. 4, p. 70-71) Definitional Formula: SS = (X - )2
Computational Formula: SS = X2 - (X)2
N
D) Variance (Ch. 4)
Population
Definitional Formula: 2
=
(X-X)2 N
Computational Formula: 2 = X2-(NX)2
N
Basic Formula: 2 = SS
N
Sample
Definitional Formula: s2 = (X-X)2
n-1
Computational Formula: s2 = X2-(nX)2
n-1
Basic Formula: s2 = SS
n-1
Population
E) Standard Deviation (Ch. 4)
Computational Formula: = X2-(NX)2
N
Basic Formula:
=
SS
N
Sample
Computational Formula: s =
X2-(nX)2
n - 1
Basic Formula: s = SS
n - 1
F) z-Score (Ch. 5)
For locating an X value's position within a sample:
z = X-
X = z +
= X-
z
For locating a sample mean's position within a population:
z = M-
M
M = zM +
M =
n
OR
M
=
2
n
Finding Degrees of Freedom
z-Scores Single Sample t-Statistic Paired / Related Sample t-Statistic Independent Samples t-Statistic Paired Samples t-Statistics
Independent Measures ANOVA:
df = n - 1
df = (n1 - 1) + (n2 - 1) df = (dfbetween), (dfwithin) dfbetween = k - 1 dfwithin = N - k
Repeated Measures ANOVA: Chi-Square:
df = (dfbetween), (dferror) dfbetween = k - 1 dferror = (N - K) - (n - 1) If single row of data: df = C - 1
If table of data: df = (R - 1)(C - 1)
?2019 Tyndale University College and Seminary. All rights reserved. Tip Sheets are for personal use only. Any unauthorized reproduction or distribution is prohibited.
4.3 2.4 2 2.5
4.4 2
3.5 1.8
3 4.3 2.4 2 2.5 4.4 2 3.5 1.8 3
CATEGORY 1 CATEGORY 2 CATEGORY 3
Intro to Statistics Formula Sheet
CATEGORY 4 CATEGORY 5 CATEGORY 6
G) Single Sample t-Statistic (Ch. 7)
t = M-
sM
sM =
s n
OR
sM
=
s2
n
H) Independent Measures & Two Samples t-Statistic (Ch. 8)
t=
(M1 - M2) - (1 - 2) sM1-M2
If
sample
sizes
are
the
same:
sM1-M2
=
s12
n1
+
s22 n2
If the sample sizes are different:
Pooled Variance:
sp2
=
SS1+ SS2 df1+ df2
sM1-M2
=
sp2
n1
+
sp2 n2
K) Pearson Correlation (Ch. 11)
SP r=
(SSx)(SSy)
(X)(Y) SP = XY - n
SSx
=
X2
-
(X)2 n
SSy
=
Y2
-
(Y)2 n
L) Chi-Square Statistic (Ch. 12)
2
=
(fo
- fe)2 fe
I) Paired Samples & Related Samples t-Statistic (Ch. 9)
t = MD-D
sMD
sMD
=
sD n
3.5 3
J) Independent Measures & Repeated Measures ANOVA (Ch. 10)
SStotal
=
X2
-
G2 N
dftotal = N - 1
2.5 2
T2 G2
SSbetween = n - N
dfbetween = k - 1
1.5
SSwithin = SSwithin (each condition)
dfwithin = N - k
1
MSbetween
=
SSbetween dfbetween
MSwithin
=
SSwithin dfwithin
F
=
MSbetween MSwithin
0.5
0
0
0.5
1
1.5
2
2.5
3
?2019 Tyndale University College and Seminary. All rights reserved. Tip Sheets are for personal use only. Any unauthorized reproduction or distribution is prohibited.
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