1 Testing Statistical Hypothesis Independent Sample t-Test Heibatollah Baghi, and Mastee Badii.
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1 Testing Statistical Hypothesis Independent Sample t- Test Heibatollah Baghi, and Mastee Badii
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Transcript of 1 Testing Statistical Hypothesis Independent Sample t-Test Heibatollah Baghi, and Mastee Badii.
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Testing Statistical HypothesisIndependent Sample t-Test
Heibatollah Baghi, and Mastee Badii
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Example of Independent Groups t-tests
• Suppose that we plan to conduct a study to alleviate the distress of preschool children who are about to undergo the finger-stick procedure for a hematocrit (Hct) determination.
• Note: Hct = % of volume of a blood sample occupied by cells.
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Example of Independent Groups t-tests, Continued
• Twenty subjects will be used to examine the effectiveness of the special treatment.
• 10 subjects randomly assigned to treatment group.
• 10 assigned to a control group that receives no special preparation.
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1. Determine the Appropriate Test
• Testing hypothesis about two independent means (t-test)– Dependent variable = the child’s
pulse rate just prior to the finger-stick– Independent variable or grouping
variable = treatment conditions (2 levels)
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1. Determine the Appropriate Test• Two samples are independent.
• Two populations are normally distributed.
• The assumption of homogeneity of variance. (Examine Levene’s Test)
Ho: 1 2 = 12
Ha: 1 2 12
If sig. level or p-value is > .05, the assumption is met.
Independent Samples Test
.134
.719
-1.847 -1.847
F
Sig.
Levene's Test forEquality of Variances
tt-test for Equality ofMeans
Equal variancesassumed
Equal variancesnot assumed
Pulse rate
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2. Establish Level of Significance
• The convention• α = .05• α = .01• α = .001
• In this example, assume α = 0.05
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3. Determine Whether to Use a One or Two Tailed Test
• H0 : µ1 = µ2
• Ha : µ1 µ2 – Where
– µ1 = population mean for the experimental group
– µ2 = population mean for the control group
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4. Calculating Test Statistics
Group 1 Group 2
1 100 105
2 86 95
3 112 120
4 80 85
5 115 110
6 83 100
7 90 115
8 94 93
9 85 107
10 105 120
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Rearrange the Data
1 100 1
2 86 1
3 112 1
4 80 1
5 115 1
6 83 1
7 90 1
8 94 1
9 85 1
10 105 1
11 105 2
12 95 2
13 120 2
14 85 2
15 110 2
16 100 2
17 115 2
18 93 2
19 107 2
20 120 2
Experimental Group
Control Group
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4. Calculating Test Statistics (continued)
67.138S 46.154S 4.
1248.03 )X- (X SS 1390.14 )X- (X SS 3.
105.0 95.0 X 2.
1050 950 X 1.
2 2
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211 221
Group 1 (Experimental) Group 2 (Control)
--------------------------------------------------------------------------------------------------
X1 X2
------------ --------------
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4. Calculating Test Statistics (continued)
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6. Compare the Computed Test Statistic Against a Tabled Value
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6. Compare the Computed Test Statistic Against a Tabled Value
• If we had chosen a one tail test:– H0 : µ1 = µ2 – Ha : µ1 < µ2
1.73
The null hypothesis can be rejected
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Independent Samples Test
.134
.719
-1.847 -1.847
18 17.948
.081 .081
-10.000 -10.000
5.414 5.414
-21.374 -21.377
1.374 1.377
F
Sig.
Levene's Test forEquality of Variances
t
df
Sig. (2-tailed)
Mean Difference
Std. Error Difference
Lower
Upper
95% Confidence Intervalof the Difference
t-test for Equality ofMeans
Equal variancesassumed
Equal variancesnot assumed
Pulse rate
Group Statistics
10 95.00 12.428 3.930
10 105.00 11.776 3.724
Group1
2
Pulse rateN Mean Std. Deviation
Std. ErrorMean
SPSS Output for Two Sample Independent t-test Example
