test for independent samples

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Week 9:Independent t-test

ttest for Two Independent Samples


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Independent Samples t- test The reason for hypothesis

testing is to gain knowledgeabout an unknownpopulation.

Independent samples t-test isapplied when we have twoindependent samples andwant to make a comparisonbetween two groups o

findividuals. The parameters

are unknown. How is this different than a Z-

test and One Sample t-test?


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Independent t- test We are interested in the difference between

two independent groups. As such, we arecomparing two populations by evaluating the

mean difference. In order to evaluate the mean difference

between two populations, we sample fromeach population and compare the sample

means on a given variable. Must have two independent groups

(i.e.samples) and one dependent variablethat is continuous to compare them on.


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Examples: Do 8th graders have significantly more

unexcused absences than 7th graders inToledo junior highs?

IV: Grade (2 groups: 8th grade and 7th grade)DV: Unexcused absences Note that Independent t-test can be applied

to answer each research question when the

independent variable is dichotomous withonly two groups and the dependent variableis continuous.


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Generate examples of research questions

requiring an Independent Samples t-test:

What are some examples that you cancome up with? Remember- you need

two independent samples and onedependent variable that is continuous.


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Assumptions The two groups are independent of one another.

The dependent variable is normally distributed. Examine skewness and kurtosis (peak) of distribution

Leptokurtosis vs. platykurtosis vs. mesokurtosis

The two groups have approximately equal

variance on the dependent variable. (When[equal sample sizes] ,the violation of thisassumption has been shown to be unimportant.)

nn 21


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Steps in Independent Samples t-test


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Step 1: State the hypotheses

Ho: The null hypothesis states that the two samples come from the samepopulation. In other words, There is no statistically significantdifference between the two groups on the dependent variable.

Symbols:

Non-directional:Ho: 1 = 2

Directional: or

If the null hypothesis is tenable, the two group means differ only bysampling fluctuationhow much the statistics value varies fromsample to sample or chance.

21:0

H21

:0

H


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Ha: The alternative hypothesis states that the twosamples come from different populations. In otherwords, There is a statistically significant difference

between the two groups on the dependent variable.

Symbols:

Non-directional:

Directional:

21

:1 H

21

:1 H

21

:1 H


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Step 2: Set a Criterion for

Rejecting Ho Compute degrees of freedom

Set alpha level

Identify critical value(s)

Table C. 3 (page 638 of text)


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Computing Degrees of Freedom Calculate degrees of freedom (df) to determine

rejection region.

df =sample size for sample1+ sample size for sample2 - 2

df describe the number of scores in a sample that arefree to vary.

We subtract 2 because in this case we have 2samples.

221

nn


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More on Degrees of Freedom

In an Independent samples t-test, eachsample mean places a restriction on the

value of one score in the sample, hencethe sample lost one degree of freedom andthere are n-1 degrees of freedom for the

sample.


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Set alpha level Set at .001, .01 , .05, or .10, etc.


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Identify critical value(s) Directional or non-directional?

Look at page 638 Table C.3.

To determine your CV(s) you need toknow: df if df are not in the table, use the next

lowest number to be conservative directionality of the test

alpha level


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Step 3: Collect data and Calculate tstatistic

nnnnnsns

xxt

2121

2

2

21

2

1

21

11

2

11

Whereby:n: Sample size s2 = variance

:Sample mean subscript1 = sample 1 or group 1

subscript2 = sample 2 or group 2

x

df

variance


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Step 4: Compare test statistic tocriterion

df = 18 = .05 , two-tailed test in this example critical values are 2.101 in this example


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Step 5: Make Decision

Fail to reject the null hypothesis and conclude that there is no statistically

significant difference between the two groups on the dependent variable,

t = , p > .

OR

Reject the null hypothesis and conclude that there is a statistically

significant difference between the two groups on the dependent variable,

t = , p < .

If directional, indicate which group is higher or lower (greater, or lessthan, etc.).


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Interpreting Output Table:

Retrieved on July 12, 2007 from SPSSShortManual.html

t-value Degrees offreedom

p- value

Levenes tests the assumption of equalvariances ifp< .05, then variancesare not equal and use a different test

to modify this:

Here, we have met

the assumption souse first row.

Observed differencebetween the groups

Mean APGARSCORE

CI

Sample size


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Interpreting APA table:


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Variable Math anxiety t

GenderMale 3.66

Female 3.98 3.35***

Age

Under 40 years 3.32

Over 41 years 3.64 2.67**

Note. **p< .01. ***p< .001.


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Examples and Practice

See attached document.

Create the following index cards from this

lecture: When to conduct a t-test (purpose, conditions,

and assumptions)

t-test statistic formula for computation

t-test statistic formula df formula

Documents

test for independent samples