[PDF] Pooled Variance t Test - gimmenotes



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Pooled Variance t Test - gimmenotes

(Variance) F Among (Methods) 4 - 1 = 3 348 116 11 6 Within (Error) 12 - 4 = 8 80 10 Total 12 - 1 = 11 428 Source of Variation Degrees of Freedom Sum of Squares Mean Square (Variance) F Among (Methods) 4 - 1 = 3 348 116 11 6 Within (Error) 12 - 4 = 8 80 10 Total 12 - 1 = 11 428

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Pooled Variance

t Test

Tests means of 2 independent populations having

equalvariances

Parametric test procedure

Assumptions

Both populations are normally distributed

If not normal, can be approximated by normal distribution (n130 & n230 )

Population variances are unknownbut assumed equal

Two Independent Populations

Examples

An economist wishes to determine whether

there is a difference in mean family income for households in 2 socioeconomic groups.

An admissions officer of a small liberal arts

college wants to compare the mean SAT scores of applicants educated in rural high schools & in urban high schools.

Pooled Variance t Test Example

to see if there a difference in dividend yield between stocks listed on the NYSE & NASDAQ.

NYSENASDAQ

Number2125

Mean3.272.53

Std Dev1.301.16

Assuming equalvariances, is

there a difference in average yield (= .05)?

© 1984-1994 T/Maker Co.

Pooled Variance t Test

Solution

H0:1 -2= 0 (1 = 2)

H1:1 -20 (1 2)

.05 df 21 + 25 -2 = 44

Critical Value(s):

Test Statistic:

Decision:

Conclusion:

t02.0154-2.0154 .025

Reject H0Reject H0

.025 t02.0154-2.0154 .025

Reject H0Reject H0

.025 2.03 25
1 21

11.510

2.533.27t

Reject at

= .05

There is evidence of a

difference in means

Test Statistic

Solution

tXX Snn SnSnS nn P P

FHGIKJ

F H I K 1212
2 12 211
2 22
2 12 22
11

3272530

15101
21
1 25
203
11 11

211130251116

2112511510

chafafaf afafafaf afafafafafaf tXX Snn SnSnS nn P P

FHGIKJ

F H I K 1212
2 12 211
2 22
2 12 22
11

3272530

15101
21
1 25
203
11 11

211130251116

2112511510

chafafaf afafafaf afafafafafaf equalvariances, is there a difference in the average miles per gallon (mpg) of two car models (= .05)?

You collect the following:

SedanVan

Number1511

Mean22.0020.27

Std Dev4.773.64

Pooled Variance t Test

Thinking Challenge

Alone Group Class

Test Statistic

Solution*

tXX Snn SnSnS nn P P

FHGIKJ

F H I K 1212
2 12 211
2 22
2 12 22
11

220020270

187931

15 1 11 100
11 11

151477111364

15111118793

chafafaf afafafaf afafafafafaf tXX Snn SnSnS nn P P

FHGIKJ

F H I K 1212
2 12 211
2 22
2 12 22
11

220020270

187931

15 1 11 100
11 11

151477111364

15111118793

chafafaf afafafaf afafafafafaf

One-Way ANOVA F-Test

2 & c-Sample Tests with

Numerical Data

2 & C-SampleTests

#Samples

Median VarianceMean

CCF Test

(2 Samples)

Kruskal-

Wallis Rank

Test

Wilcoxon

Rank Sum

Test #Samples

Pooled

Variance

t Test

One-Way

ANOVA 22

2 & C-SampleTests

#Samples

Median VarianceMean

CCF Test

(2 Samples)

Kruskal-

Wallis RankTest

Wilcoxon

Rank SumTest

#Samples

Pooled

Variancet Test

One-Way

ANOVA 22

Experiment

Investigator controls one or more independent

variables

Called treatment variables or factors

Contain two or more levels (subcategories)

Observes effect on dependent variable

Response to levels of independent variable

Experimental design: Plan used to test

hypotheses

Completely Randomized Design

Experimental units (subjects) are assigned

randomly to treatments

Subjects are assumed homogeneous

One factor or independent variable

2 or more treatment levels or classifications

Analyzed by:

One-Way ANOVA

Kruskal-Wallis rank test

Factor (Training Method)

Factor levels

(Treatments)

Level 1Level 2Level 3

Experimental

units

Dependent21 hrs.17 hrs.31 hrs.

variable27 hrs.25 hrs.28 hrs. (Response)29 hrs.20 hrs.22 hrs.

Factor (Training Method)

Factor levels

(Treatments)

Level 1Level 2Level 3

Experimental

units

Dependent21 hrs.17 hrs.31 hrs.

variable27 hrs.25 hrs.28 hrs. (Response)29 hrs.20 hrs.22 hrs.

Randomized Design Example

One-Way ANOVA

F-Test

Tests the equality of 2 or more (c) population

means

Variables

One nominal scaled independent variable

2 or more (c) treatment levels or classifications

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