09 - Hypothesis Testing With t Tests

8/12/2019 09 - Hypothesis Testing With t Tests

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Hypothesis Testing withHypothesis Testing with tt TestsTestsr o ar - oos


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Using Samples to EstimateUsing Samples to Estimate

Population ParametersPopulation Parameters Acknowled e error

Smaller samples, less spread2

1

=

N

s


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Hypothesis Tests:Hypothesis Tests:

SingleSingle--SampleSample tt TestsTests

Guinness is the best beer available, it does

not nee a vertising as its qua ity wi se it,and those who do not drink it are to be

.


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..


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1. Identif

2. State the hypotheses.

distribution

.

5. Calculate

6. Decide


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-- Partici ation in thera sessions

Contract to attend 10 sessions= .

Sample:

6, 6, 12, 7, 8


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--1. Identif

Pop 1: All clients who sign contract Po 2: All clients who do not si n contract

Distribution of means

standard deviation single-sample t test

Assumptions


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--2. State the null and research h otheses

H0: Clients who sign the contract will attendthe same number of sessions as those who

do not sign the contract.

1 = 2

H1: Clients who sign the contact will attend

a different number of sessions than those

.

1

2


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--3. Determine characteristics of

comparison distribution= = 4.6 2

sM

= 1.114 490.2

1

=

=

N

s

114.1490.2

=== s

sM


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--4. Determine critical values or cutoffs

df = N-1 = 5-1 = 4, p = .05 t = 2.776


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--5. Calculate the test statistic

873.2)6.48.7()(

=== MM

t

.M

6. a e a ec s on

2.873 > 2.776, we reject the null

Clients who sign a contract will attend moresessions than those who do not sign a

.


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1. Write the symbol for the test statistic (e.g.,z

or t)2. Write the degrees of freedom in parentheses

3. Write an equal sign and then the value of the

test statistic (2 decimal places)4. Write a comma and then whether the p value

associated with the test statistic was less than

.

= . , .


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Conditions must be e uivalent

(controlled) for a fair test

Beer Tasting: Between-groups vs. Within-groups


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-- Used to com are 2 means for a within-

groups design, a situation in which everyartici ant is in both sam les

(paired/dependent)

Difference Scores:X1Y1, X2Y2,


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--1. Identif

2. State null & research hyp..

comparison distribution

0 1 2


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--4. Determine cutoffs

5. Calculate test statistic

M

M

st=

6. a e a ec s on


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Used to com are 2 means for a between-

groups design, a situation in which eachartici ant is assi ned to onl one condition.


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What ercenta e of cartoons do men and

woman consider funny?

Women: 84 97 58 90 Men: 88 90 52 97 86


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1. Identif

Population 1: Women exposed to humorouscartoons

Population 2: Men exposed to humorous

cartoons Distribution: Differences between means

Not mean differences

Assumptions are the same We meet one here: DV is interval/scale


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2. State null and research

hypotheses H0:1 = 2

Women will categorize the

same number of cartoons as.

H1:1 2

Women will cate orize a

different number of cartoonsfunny as as will men.


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3. Determine characteristics of

comparison distribution H0:1 = 2 Measure of spread:

a) Calculate variance for each sample

,

c) Convert from squared standard deviation tosquared standard error

d) Add the two variancese) Take square root to get estimated standard error


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a) Calculate variance for each sample

22 ( ) 868.752 289.584X

X Ms

= = =

2 .328.61 5 1

Ys N= = =


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De rees of Freedom

= = =

Y= = =

dfTotal= dfX+ dfY= 3 + 4 = 7


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b) Pool variances, accounting for sample size

Weighted average of the two estimates of variance one from each sample that are calculated when

con uct ng an n epen ent samp es t test.

d dPooled X Y

Total Total

s s sdf df

= +

2 289.584 328.67 7

Pooleds = +

2

124.107 187.771 311.878Pooleds = + =


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c Convert from s uared standard deviation to

2 311.878Pooled

s =2 2

squared standard error

2 . 77.9704X

PooledMs

N= = = 2

.62.376

5YPooled

Ms

N= = =

2 2 2 77.970 62.376 140.346X YDifference M M

s s s= + = + =

e) Take square root to get estimated standard error for

distribution of differences between means.

2 140.346 11.847Difference Differences s= = =


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4. Determine critical values

dfTotal= 7 p = .05 t = 2.365

5. Calculate a test statistic

( )X Y X Y X Y

Difference Difference

M Mt

s s

= =

( )82.25 82.6.03t

= =

.


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6. Make a decision

Men and women find cartoons equallyhumorous

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09 - Hypothesis Testing With t Tests