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.