GEM2900 Cheat Sheet 2

Usage Standard Error & Rule of Thumb p-value

Assumptions

Check whether two group means are different

Assume two groups A &B have similar SSD not too different in size Probability that test is as extreme or > extreme than observed data

Calculations

SE=

√

p ( 1−p ) SSD = n √n

Interpretations Example Strong indication that two group means are different if the intervals

SM A ± 1.5 ×SE A One-sided: Only interested in bias towards H

¿ P ( t=9,t=10, t=1,t=0 )

H1:

10 1 10 1 + + + =0.021 1024 1024 1024 1024

if n>30, 0.2< p > P (T ) 2

H1:

1 P( H )≠ ≠ P(T ) 2

Given : X 1 N ( m1 , s 1) ∧X 2 N ( m2 , s 2 ) independent Let X N ( 102.6,18.5 ) . What is P ( X ≤

Gaussian distribution

Z=

P ( X ≤ 120 )=P ( N ( 102.6,18 .5 ) ≤ 120 )

X 1 + X 2 N (m 1+ m 2 , √ s 21+ s 22)

W −np √ np ( 1− p )

¿ P ( N ( 0,18.5 ) ≤ 17.4 ) ¿ P ( N ( 0,1 ) ≤ 0.940 ) ≈ 0.8264

Sign Test (Proportion)

t-test (Means)

χ2

and

contingency tables

Used to test that the difference median is zero between two variables Decide whether group means are different

Test independence between two variables

Assume

n

independent pairs of observations

Assume

ρ

ranking

(Correlation)

()

independent measurements following a Gaussian distribution. Assume each group same SD. There’s no one-sided or two-sided test for

χ2

t=

SM A −SM B

√ SE A + SE B 2

2

, df =2 n−2

df =(rows−1)(col−1) Check for correlation between two variables

Assume

n

independent pairs of observations

20

( 12 ) ((2014)+( 2015)+ …)

P (W ≥ 14 )=

When given SM, SSD, and n, t-test can be used to decide whether the two means are different. If SSD are different, t-test is not as accurate

( Original−Expected )2 χ =∑ Expected 2

6 ∑ D i2 ρ=1− n(n2−1) df =n−2

After introducing airbags, no. of casualties in accidents dropped in 14 among 20 countries and gone up in other 6

To find

H0: No difference between the two H1: The two are different

n

(Independenc e)

Spearman’s

n−k P (W =k )= n pk ( 1− p ) k

Observed F M N 68 64 13 2 Y 82 130 21 2 150 194 34 4 Before 35 38 3 4 After 76 56 8 4 Di -5 0 2

Di

25

0

Expected F M N 57.56 74.4

The proportion of Samsung versus Apple smartphones owners in Singapore is different than as compared to Malaysia.

132

Y 92.44 119.56 212 150

194

It was observed that the average PSI on rainy days is lower than the average PSI on sunny days

344

43 6 58 5 1

33 2 63 6 -4

45 7 36 1 6

52 8 48 2 6

32 1 55 3 -2

42 5 75 7 -2

1

16

36

36

4

4

Do taller students have a higher CAP?

Sample Mean , x=

SSD=

√

x 1+ x2 +…+ xn n

2 2 2 ( x 1−x ) + ( x 2−x ) +…+ ( xn −x )

n−1

SSD is standard deviation of ONE individual from the sample mean SE is the standard deviation of the sample mean from the population