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.

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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

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?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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