# Hypotheses Testing & T-test

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```					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.   Determine hypotheses (null & alternative)
2.   Select significance level ( level/p level)
3.   Choose a sample size
4.   Calculate the value of the statistic
5.   Obtain critical value
6.   Compare results

BAD 6243: Applied Univariate Statistics   2
Errors in Hypothesis Testing
Decision               When H0 is                       When H0 is
“true”                           “false”

Reject H0              Type I error (,                 Correct decision
Sample (“Trial”)

significance level)              (1 - , confidence
level)

Fail to reject H0      Correct decision                 Type II error ()
(1-, power level)

Population (“Truth”)
BAD 6243: Applied Univariate Statistics                        3
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
BAD 6243: Applied Univariate Statistics          4
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
BAD 6243: Applied Univariate Statistics   5
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
BAD 6243: Applied Univariate Statistics   6
Standard Normal Distribution

BAD 6243: Applied Univariate Statistics   7
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
BAD 6243: Applied Univariate Statistics                 8
Independent Samples t-test
Group Statistics

Std. Error
Gender                    N           Mean          Std. Deviation           Mean
Starting Salary Female                        469   24769.51            6895.765            318.417
Male                          631   27026.51            6870.097            273.494

Independent Samples Test

Levene's Test for
Equality of Variances                                 t-test for Equality of Means
95% Confidence
Interval of the
Mean       Std. Error        Difference
F          Sig.        t             df     Sig. (2-tailed)   Difference   Difference    Lower        Upper
Starting Salary Equal variances
.034        .854     -5.380         1098            .000      -2257.00      419.517 -3080.142 -1433.850
assumed
Equal variances
-5.377     1006.360            .000      -2257.00      419.748 -3080.678 -1433.314
not assumed

BAD 6243: Applied Univariate Statistics                                                 9
Independent Samples Error Bar
28000

27000

26000

25000

24000

23000
N=                      469                      631

Female                      Male

Gender
BAD 6243: Applied Univariate Statistics    10
T-test as a Regression Model
Model Summary

Adjusted          Std. Error of
Model        R       R Square         R Square         the Estimate
1             .160 a     .026             .025            6881.049
a. Predictors: (Constant), Gender

ANOVAb

Sum of
Model                  Squares        df       Mean Square           F           Sig.
1        Regression   1.37E+09            1     1370474872          28.944         .000 a
Residual     5.20E+10         1098    47348835.43
Total        5.34E+10         1099
a. Predictors: (Constant), Gender
b. Dependent Variable: Starting Salary
Coefficientsa

Unstandardized        Standardized
Coefficients          Coefficients
Model                   B        Std. Error       Beta               t          Sig.
1        (Constant) 24769.510     317.737                          77.956         .000
Gender      2256.996     419.517              .160         5.380         .000
a. Dependent Variable: Starting Salary

BAD 6243: Applied Univariate Statistics                               11
Dependent Samples T-test
Paired Samples Statistics

Std. Error
Mean                      N        Std. Deviation        Mean
Pair       Starting Salary 26064.20                    1100         6967.982         210.093
1          Current Salary 27404.39                     1100         7363.757         222.026

Paired Samples Correlations

N          Correlation         Sig.
Pair      Starting Salary &
1100              .994           .000
1         Current Salary

Paired Samples Test

Paired Differences
95% Confidence
Interval of the
Std. Error         Difference
Mean      Std. Deviation     Mean         Lower        Upper        t            df     Sig. (2-tailed)
Pair   Starting Salary -
-1340.19        856.541       25.826      -1390.86     -1289.51    -51.894        1099            .000
1      Current Salary

BAD 6243: Applied Univariate Statistics                                          12
Dependent Samples Error Bar
27600

27400

27200

27000

26800

26600

26400

26200
95% CI

26000

25800
N=               1100                   1100

SAL1                   SAL2

BAD 6243: Applied Univariate Statistics   13

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