PARAMETRIC TESTS FOR COMPARING TWO GROUPS
NORBERTO E. MILLADepartment of StatisticsVisayas State University
Is there a significant difference in the performance of students in the experimental and control groups?
Is there a significant increase in the level of morale of employees after attending the seminar-workshop?
Is there a difference in the biodiversity indices between logged and unlogged forests?
Dependent groups- also known as paired or matched samples
Pre-Post Test design: same variable is measured on two different occasions (pre and post) using similar instruments on a group of subjects
Matched-pairs design: pairs of comparablesubjects are used; within each pair, subjects are randomly assigned to two treatment conditions
T test (for independent groups) when variances are statistically equalT test (for independent groups) when variances are statistically unequalWelch T testT test (for dependent groups)-also known as paired-samples T test; data must be encoded in Stata in wide formatData must be at least interval in scale of measurement
NORMAL DATA
Statistics >> Summaries, tables, and tests >> Distributional plots and tests>> Shapiro-Wilk normality test
Interpretation: The distribution of self-efficacy (content knowledge)
scores of females (p=0.4607) and males (p=0.1782) are normally
distributed.
se_ck 14 0.91369 1.597 0.922 0.17824
Variable Obs W V z Prob>z
Shapiro-Wilk W test for normal data
-> sex = Male
se_ck 67 0.98238 1.047 0.099 0.46070
Variable Obs W V z Prob>z
Shapiro-Wilk W test for normal data
-> sex = Female
OUTPUT
Statistics >>Summaries, tables, and tests >>Classical tests of hypotheses >>Variance comparison test
Interpretation: There is significant difference between the variances of self-
efficacy scores of males and females (F=0.4382, p=0.0148).
Pr(F < f) = 0.0148 2*Pr(F < f) = 0.0296 Pr(F > f) = 0.9852
Ha: ratio < 1 Ha: ratio != 1 Ha: ratio > 1
Ho: ratio = 1 degrees of freedom = 66, 13
ratio = sd(Female) / sd(Male) f = 0.4382
combined 81 3.629012 .0628592 .5657332 3.503918 3.754106
Male 14 3.460714 .2068988 .7741443 3.013737 3.907692
Female 67 3.664179 .0626095 .512481 3.539175 3.789183
Group Obs Mean Std. Err. Std. Dev. [95% Conf. Interval]
Variance ratio test
OUTPUT
Pr(F < f) = 0.1741 2*Pr(F < f) = 0.3483 Pr(F > f) = 0.8259
Ha: ratio < 1 Ha: ratio != 1 Ha: ratio > 1
Ho: ratio = 1 degrees of freedom = 66, 13
ratio = sd(Female) / sd(Male) f = 0.7043
combined 81 2.800617 .0485793 .4372138 2.703941 2.897293
Male 14 2.764286 .1354103 .5066589 2.47175 3.056822
Female 67 2.808209 .0519476 .4252091 2.704492 2.911926
Group Obs Mean Std. Err. Std. Dev. [95% Conf. Interval]
Variance ratio test
Interpretation: There is no significant difference between the variances of
pedagogical strategy scores of males and females (F=0.7043, p=0.1741).
OUTPUT
Statistics >> Summaries, tables, and tests >> Classical tests of hypotheses >> t test (mean-comparison test)
Pr(T < t) = 0.8196 Pr(|T| > |t|) = 0.3607 Pr(T > t) = 0.1804
Ha: diff < 0 Ha: diff != 0 Ha: diff > 0
Ho: diff = 0 Welch's degrees of freedom = 15.84
diff = mean(Female) - mean(Male) t = 0.9413
diff .2034648 .2161644 -.2551598 .6620895
combined 81 3.629012 .0628592 .5657332 3.503918 3.754106
Male 14 3.460714 .2068988 .7741443 3.013737 3.907692
Female 67 3.664179 .0626095 .512481 3.539175 3.789183
Group Obs Mean Std. Err. Std. Dev. [95% Conf. Interval]
Two-sample t test with unequal variances
Interpretation: There is no significant difference between the mean efficacy
scores of males and females (t=0.9413, p=0.1804).
OUTPUT
Statistics >> Summaries, tables, and tests >> Classical tests of hypotheses >> t test (mean-comparison test)
Pr(T < t) = 0.6326 Pr(|T| > |t|) = 0.7348 Pr(T > t) = 0.3674
Ha: diff < 0 Ha: diff != 0 Ha: diff > 0
Ho: diff = 0 degrees of freedom = 79
diff = mean(Female) - mean(Male) t = 0.3400
diff .0439232 .1291959 -.2132349 .3010813
combined 81 2.800617 .0485793 .4372138 2.703941 2.897293
Male 14 2.764286 .1354103 .5066589 2.47175 3.056822
Female 67 2.808209 .0519476 .4252091 2.704492 2.911926
Group Obs Mean Std. Err. Std. Dev. [95% Conf. Interval]
Two-sample t test with equal variances
Interpretation: There is no significant difference between the mean pedagogical
strategy scores of males and females (t=0.3400, p=0.3674).
OUTPUT
Pre-Post Test design: same variable is measured on two different occasions (pre and post) using similar instruments on a group of subjects
Matched-pairs design: pairs of comparablesubjects are used; within each pair, subjects are randomly assigned to two treatment conditions
diff12 10 0.92117 1.215 0.340 0.36679
Variable Obs W V z Prob>z
Shapiro-Wilk W test for normal dataOUTPUT
Interpretation:
The pairwise differences
between the scores in
Period 1 and Period 2
are normally distributed
(W=0.9211, p=0.3668).
Statistics >> Summaries, tables, and tests >> Classical tests of hypotheses >> t test (mean-comparison test)
Interpretation: There is significant increase in the students’ mean score
from Period 1 to Period 2 (t=4.44, p=0.0008).
Pr(T < t) = 0.9992 Pr(|T| > |t|) = 0.0016 Pr(T > t) = 0.0008
Ha: mean(diff) < 0 Ha: mean(diff) != 0 Ha: mean(diff) > 0
Ho: mean(diff) = 0 degrees of freedom = 9
mean(diff) = mean(test2 - test1) t = 4.4403
diff 10 17.7 3.986226 12.60555 8.68253 26.71747
test1 10 58 3.977716 12.57864 49.00178 66.99822
test2 10 75.7 4.174127 13.19975 66.25747 85.14253
Variable Obs Mean Std. Err. Std. Dev. [95% Conf. Interval]
Paired t test
OUTPUT
Statistical significance refers to the unlikelihood that mean differences observed in the sample have occurred due to sampling error.
Given a large enough sample, despite seemingly small population differences, one might still find statistical significance.
Practical significance looks at whether the difference is large enough to be of value in a practical sense.
Statistical significance does not always imply practical significance.