Statistical Fundamentals:
Using Microsoft Excel for Univariate and Bivariate Analysis
Alfred P. Rovai
Hypothesis Testing
PowerPoint Prepared by
Alfred P. Rovai
Microsoft® Excel® Screen Prints Courtesy of Microsoft Corporation.
Presentation © 2013 by Alfred P. Rovai
Hypothesis
Testing
A hypothesis test is a statistical method used to reach
a conclusion that extends beyond the sample
measured to a target population.
To determine the accuracy of a conclusion with 100%
accuracy requires examination of an entire population
(i.e., a census). This is often not feasible for large
populations, e.g., all undergraduate university students
in the state of Virginia or all workers who abuse drugs,
because of time and cost considerations.
Instead, a sample is drawn from the target population,
the sample is measured and analyzed, a conclusion is
reached regarding the sample, and the conclusion is
extended to the population. There is always a chance
of error because the entire population was not
examined.
Copyright 2013 by Alfred P. Rovai
Sampling
Identify the target population
Obtain a list of the target population (sampling
frame)
Identify a method for selecting units from the
sampling frame that is representative of the target
population
Determine the sample size
Conduct the sampling
Copyright 2013 by Alfred P. Rovai
Identify Statistical Hypotheses
Research Hypothesis
Null Hypothesis
(H1 or HA)
(H0)
• Related to the research
question; the outcome that
the researcher desired or
expected
• For example, H1: There is a
difference in mean
computer confidence
posttest between male and
female university students,
μ1 ≠ μ2
• Opposite of the research
hypothesis; maintains the
status quo; no difference or
relationship
• For example, Ho: There is
no difference in mean
computer confidence
posttest between male and
female university students,
μ1 = μ2
Copyright 2013 by Alfred P. Rovai
Purposes of Hypotheses
Link theory with the problem
statement
Enable the researcher to objectively
enter areas of discovery
Provide direction to the research by
identifying the expected outcome
Copyright 2013 by Alfred P. Rovai
Important Interrelationships
Research
Hypothesis
Problem
Statement
Literature
Review
Theoretical
Framework
Copyright 2013 by Alfred P. Rovai
Reaching a Statistical Conclusion
1
2
3
• Statistical hypotheses are stated (H0 and H1)
• Ho is tested using an appropriate hypothesis test
• Ho is considered true unless the statistical
evidence suggests that it is false. If false, one
concludes that there is evidence to reject Ho
and accept the research hypothesis.
Copyright 2013 by Alfred P. Rovai
One- and Two-Tailed Hypotheses
One-Tailed Hypothesis
• Hypothesis is directional, e.g.,
Ho: Male university students
have a greater computer
confidence posttest mean than
female university students,
μMales > μFemales.
• The test determines whether or
not the mean of a specified
group is greater than the mean
of the other group.
Two-Tailed Hypothesis
• Hypothesis is nondirectional,
e.g., Ho: There is no difference
in mean computer confidence
posttest between male and
female university students,
μMales = μFemales.
• The hypothesis test determines
whether or not the mean of one
group is either less than or
greater than the mean of the
second group.
• Many researchers believe that
two-tailed tests should always
be used, even when making
directional predictions.
Copyright 2013 by Alfred P. Rovai
Key Points
A statistical hypothesis ALWAYS refers to the population, not the sample that is
measured. It ALWAYS refers to a parameter, e.g., μ, and never a statistic, e.g., M
A hypothesis test ALWAYS starts by assuming Ho is true
The purpose of the hypothesis test is to seek evidence that supports rejecting Ho
and accepting H1
A statistically significant hypothesis test occurs when there is statistical evidence
to reject Ho
NEVER conclude Ho is true since there is always a chance of error. Rather,
conclude, if warranted, that there is insufficient evidence to reject Ho
Copyright 2013 by Alfred P. Rovai
Choose a Significance Level
The significance level is the probability of making a Type I error
(α); that is, falsely rejecting a true Ho
An à priori value significance level is determined before one
conducts any hypothesis test
• This value is typically set at .05 for social science research and becomes
the standard for rejecting or failing to reject Ho
• A significance level of .05 means that one is willing to accept an error of
no more than 5 out of 100 in rejecting Ho
Analysis of sample data results in a p-value (probability value);
that is, the probability of falsely rejecting the true Ho
• If the p-value > the à priori significance level there is insufficient evidence
to reject Ho
• If the p-value <= the à priori significance level there is sufficient evidence
to reject Ho
Copyright 2013 by Alfred P. Rovai
Statistical Power of a Test
• Statistical power (or observed power or sensitivity)
of a statistical test is the probability of rejecting a
false H0.
-
-
Equals 1 minus the probability of accepting a false H0 (1 –
β).
Represents the degree one is willing to make a Type II
error.
• The desired standard is 80 percent or higher, leaving
a 20 percent chance, or less, of error.
Copyright 2013 by Alfred P. Rovai
Statistical Decisions
Ho is True
Ho is False
Reject Ho:
Reject Ho:
No Error
Type I error (α)
Fail to Reject Ho:
No Error (1 – α)
(1 – β)
Fail to Reject Ho:
Type II Error: (β)
Copyright 2013 by Alfred P. Rovai
Decision Errors
Setting a more liberal à priori
significance level, e.g., α = .10
- Increases the probability of a Type I
error.
- Decreases the probability of a Type II
error.
Setting a more conservative à
priori significance level, e.g., α =
.001
- Decreases the probability of a Type I
error.
- Increases the probability of a Type II
error.
Copyright 2013 by Alfred P. Rovai
Statistical Significance
Statistical significance does not imply an effect is meaningful or important.
While statistical significance is concerned with whether a statistical result is due to
chance, practical significance is concerned with whether the result is useful in the
real world.
Effect size is a measure of the magnitude of a treatment effect and is used to
assess practical significance. There is no practical significance without statistical
significance.
Effect size is the degree to which H0 is false.
Effect size can be measured in one of several ways.
Copyright 2013 by Alfred P. Rovai
Two Common Effect Size Measures
Cohen’s d (standardized
difference between two
means).
Small, d = .20
Medium, d = .50
Large, d = .80
Pearson r (correlation
coefficient between two
continuous variables).
Between 0 and ±0.20 –
Very weak
Between ±0.20 and
±0.40 – Weak
Between ±0.40 and
±0.60 – Moderate
Between ±0.60 and
±0.80 – Strong
Between ±0.80 and
±1.00 – Very strong
Note: other interpretive guides exist in the professional literature.
Copyright 2013 by Alfred P. Rovai
Methods of Increasing Statistical Power
Increase the sample size
Increase the significance level, e.g., .05 to .10
Use all the information provided by the data, e.g., do not
transform interval scale variables to ordinal scale variables
Use a one-tailed versus a two-tailed test
Use a parametric versus nonparametric test
Copyright 2013 by Alfred P. Rovai
Hypothesis Testing Steps
1
• Restate the research question as Ho and H1
2
• Decide on the à priori significance level
3
• Choose an appropriate hypothesis test
4
• Select & measure a sample from the target population
5
• Conduct the hypothesis test and state a conclusion
6
• Communicate the findings and implications for practice
Copyright 2013 by Alfred P. Rovai
Statistical Conclusion
Every hypothesis test will result
in one of two conclusions:
• There is sufficient evidence to reject
H0
• There is insufficient evidence to reject
H0
NEVER accept H0 since
there is always a chance of
error
Copyright 2013 by Alfred P. Rovai
Research Conclusion
• The conclusion reached by hypothesis test
must also be expressed in terms of the
research problem and implications for
practice.
Copyright 2013 by Alfred P. Rovai
Hypothesis
Testing
End of
Presentation
Copyright 2013 by Alfred P. Rovai