Download and T-tests

B AD 6243: Applied Univariate Statistics
Hypothesis Testing and the T-test
Professor Laku Chidambaram
Price College of Business
University of Oklahoma
Steps in Hypothesis Testing
1.
2.
3.
4.
5.
6.
Determine hypotheses (null & alternative)
Select significance level ( level/p level)
Choose a sample size
Calculate the value of the statistic
Obtain critical value
Compare results
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Sample (“Trial”)
Errors in Hypothesis Testing
Decision
When H0 is
“true”
When H0 is
“false”
Reject H0
Type I error (,
significance level)
Correct decision
(1 - , confidence
level)
Fail to reject H0
Correct decision
(1-, power level)
Type II error ()
Population (“Truth”)
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MAXMINCON Principle
• Maximize experimental variance
– Design, plan and conduct research so that the experimental
conditions are as different as possible
• Minimize error variance
– Reduce error through controlling experimental conditions
– Reduce error by increasing reliability of measures
• Control extraneous variance
– Randomization: Groups can be considered statistically equal in
all possible ways
– Selection: To eliminate the effect of an extraneous variable on a
dependent variable, choose subjects so that they are as
homogenous as possible (on that variable)
– Addition: To control the effect of an extraneous variable, build it
into the research design, so as to measure its effect on the
dependent variable
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Differences between Groups
• Randomized groups
– Random sampling; random assignment
– Simple vs. factorial designs
– Concerns:
• (Pre-experimental) equality of groups
• Unequal cell sizes
• Correlated group(s)
– Use same units in different treatments
– Single vs. multi-group designs
– Concerns:
• History, maturation and sensitization
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Concepts Related to the T-test
• Degrees of freedom
• T-distribution vs. standard normal
distribution
• Level of significance
• Between subjects design:
– Equal sample sizes
– Equal variance
• Within subjects design
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Standard Normal Distribution
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t Distributions
t-distributions refer to a family of distributions, which like normal distributions, are
bell-shaped, but whose shape changes with the sample size; smaller sample
sizes have flatter distributions, while larger sizes approximate normal distributions
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Independent Samples t-test
Group Statistics
Starting Salary
Gender
Female
Male
N
469
631
Mean
24769.51
27026.51
Std. Deviation
6895.765
6870.097
Std. Error
Mean
318.417
273.494
Independent Samples Test
Levene's Test for
Equality of Variances
F
Starting Salary Equal variances
assumed
Equal variances
not assumed
.034
Sig.
.854
t-test for Equality of Means
t
df
Sig. (2-tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower
Upper
-5.380
1098
.000
-2257.00
419.517 -3080.142 -1433.850
-5.377
1006.360
.000
-2257.00
419.748 -3080.678 -1433.314
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Independent Samples Error Bar
28000
27000
26000
25000
24000
23000
N=
469
631
Female
Male
Gender
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T-test as a Regression Model
Model Summary
Model
1
R
R Square
.160 a
.026
Adjus ted
R Square
.025
Std. Error of
the Es timate
6881.049
a. Predictors : (Constant), Gender
ANOVAb
Model
1
Regress ion
Res idual
Total
Sum of
Squares
1.37E+09
5.20E+10
5.34E+10
df
1
1098
1099
Mean Square
1370474872
47348835.43
F
28.944
Sig.
.000 a
t
77.956
5.380
Sig.
.000
.000
a. Predictors : (Constant), Gender
b. Dependent Variable: Starting Salary
Coefficientsa
Model
1
Uns tandardized
Coefficients
B
Std. Error
(Cons tant) 24769.510
317.737
Gender
2256.996
419.517
Standardized
Coefficients
Beta
.160
a. Dependent Variable: Starting Salary
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Dependent Samples T-test
Paired Samples Statistics
Pair
1
Starting Salary
Current Salary
Mean
26064.20
27404.39
N
1100
1100
Std. Error
Mean
210.093
222.026
Std. Deviation
6967.982
7363.757
Paired Samples Correlations
N
Pair
1
Starting Salary &
Current Salary
Correlation
1100
Sig.
.994
.000
Paired Samples Test
Paired Differences
Mean
Pair
1
Starting Salary Current Salary
-1340.19
Std. Deviation
Std. Error
Mean
856.541
25.826
95% Confidence
Interval of the
Difference
Lower
Upper
-1390.86
-1289.51
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t
-51.894
df
1099
Sig. (2-tailed)
.000
12
Dependent Samples Error Bar
27600
27400
27200
27000
26800
26600
26400
95% CI
26200
26000
25800
N=
1100
1100
SAL1
SAL2
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