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Statistical Fundamentals:
Using Microsoft Excel for Univariate and Bivariate Analysis
Alfred P. Rovai
One-Sample t-Test
PowerPoint Prepared by
Alfred P. Rovai
Microsoft® Excel® Screen Prints Courtesy of Microsoft Corporation.
Presentation © 2015 by Alfred P. Rovai
One-Sample t-Test
• The one-sample t-test, also known as the single-sample t-test,
is a parametric procedure that compares a calculated sample
mean to a known population mean or a previously reported
value in order to determine if the difference is statistically
significant. For example, an educational researcher might want
to determine if the mean sense of classroom community score
among university students enrolled in fully online programs
differs significantly from the hypothesized population score of
30.
• Excel data entry for the one-sample t-test is accomplished by
entering the value for each case of the variable of interest in a
single column of an Excel spreadsheet.
Copyright 2015 by Alfred P. Rovai
One-Sample t-Test
• One can compute the t-value using the following formula:
t=
(X - X0 )
SX
N
where the numerator is the difference in group means and the
test value and the denominator is the estimated standard error
of the sample divided by the square root of the sample size.
Copyright 2015 by Alfred P. Rovai
One-Sample t-Test
• Cohen’s d measures effect size and is often used to report
effect size following a significant t-test. The formula for
Cohen’s d for the one-sample t-test is:
t
d=
N
• By convention, Cohen’s d values are interpreted as follows:
– Small effect size = .20
– Medium effect size = .50
– Large effect size = .80
Copyright 2015 by Alfred P. Rovai
Key Assumptions & Requirements
• Random selection of samples to allow for generalization of
results to a target population.
• Variables. One continuous dependent variable (DV) measured
on the interval or ratio scale.
• Independence of observations. observations (i.e.,
measurements) are not acted on by an outside influence
common to two or more measurements.
• Normality. One DV normally distributed.
• Sample size. The one-sample t-test is robust to minor
violations of the assumption of normally distributed data with
sample sizes > 30.
Copyright 2015 by Alfred P. Rovai
Conducting the One-Sample t-Test
Open the dataset Motivation.xlsx. Click
on the One-Sample t-Test worksheet tab.
File available at
http://www.watertreepress.com/stats
TASK
Respond to the following research question
and null hypothesis:
Is there a difference in the mean sense of
classroom community (c_community) score
among university students enrolled in fully
online programs and the norm of 30, μ ≠ 30?
H0: There is no difference in the mean sense
of classroom community score of university
students enrolled in fully online programs
and the norm of 30, μ = 30.
Copyright 2015 by Alfred P. Rovai
Go to the One-Sample t-Test tab of the Motivation 3rdEd.xlsx Excel workbook. Enter the
labels and formulas shown in cells B1:C13. Note: cell C4 contains the test value from the
null hypothesis.
Copyright 2015 by Alfred P. Rovai
Test Results Summary
Test results provide evidence that there is sufficient evidence (p = 0.02) to reject
the null hypothesis that there is no difference in the mean sense of classroom
community score of university students enrolled in fully online programs and the
norm of 30.
Copyright 2015 by Alfred P. Rovai
Reporting One-Sample t-Test Results
As a minimum, the following information should be reported in the results section
of any research report: null hypothesis that is being evaluated to include test
value, descriptive statistics (e.g., M, SD, N), statistical test used (i.e., one-sample ttest), results of evaluation of test assumptions, as appropriate, and test results.
For example, one might report test results as follows. The formatting of the
statistics in this example follows the guidelines provided in the Publication Manual
of the American Psychological Association (APA).
Results
A one-sample t-test was conducted to evaluate the null hypothesis that there is no
difference in the mean sense of classroom community score of university students
enrolled in fully online programs and the norm of 30 (N = 169). The test showed
that the sample mean (M = 28.84, SD = 6.24) was significantly different than the
test value of 30, t(168) = 2.42, p = .02 (2-tailed), d = .19. Consequently, there was
sufficient evidence to reject the null hypothesis.
Copyright 2015 by Alfred P. Rovai
OneSample tTest
End of
Presentation
Copyright 2015 by Alfred P. Rovai