09 - Hypothesis Testing With t Tests
Transcript of 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