1. A statistical hypothesis represents the mathematical relationship between two or more population parameters. It can be directional, specifying the exact relationship, or nondirectional, anticipating a difference but not specifying the direction. 2. The null hypothesis predicts no difference between population parameters, while the alternative or experimental hypothesis predicts a difference. Through statistical testing, we can either reject the null hypothesis in favor of the alternative, or accept the null hypothesis. 3. Significance testing uses statistical tests and probabilities to determine if sample data can be used to reject the null hypothesis involving population parameters. If the difference is unlikely to have occurred by chance when the null hypothesis is true, it is considered statistically significant.

1. STATISTICAL HYPOTHESIS
Desmond Ayim-Aboagye, Ph.D.
Quantifying the relationship between
the variables involved in the conceptual
and operational hypothesis

2. The Null and Experimental Hypothesis
• A Statistical hypothesis represents the mathematical
relationship presumed to exist between two or more
population parameters.
• A. Symbolic form (𝝁c ˃ 𝝁e)
• B. Written form
• (The average number of correctly recognized changes
for the control group (𝝁c) is anticipated to be higher
than changes noted by the experimental group (𝝁e) )
•

3. Directional and Nondirectional
Hypothesis
• Relationship existing between the population
parameters identified in any statistical
hypothesis can be one or two types.
• 1. Directional
• 2. Nondirectional

4. Directional hypothesis
• A directional hypothesis specifies the exact
nature or direction of the relationship
between population parameters.
• (𝝁c ˃ 𝝁e) or (𝝁c < 𝝁e)
• ≤ or ≥ less than or equal to or greater than or
equal to can also be used.

5. Nondirectional hypothesis
• A nondirectional hypothesis anticipates a
difference will exist between population
parameters but does not specify the nature,
or direction, of that difference.
• Symbolically (𝝁c ≠ 𝝁e)
• Note: the representative magnitudes of the
population means are not specified by this
relationship

6. Null hypothesis and Experimental
hypothesis
• Logicians, philosophers, scientists, and
statisticians all agree that:
• Empirical statements can never be proved to
be true, but they can be demonstrated to be
false.
• Take dogs barking as example. "They all bark"

7. Null hypothesis
• The null hypothesis traditionally indicates all
the population in an experiment, which are
represented by sample statistics, are equal.
The null hypothesis predicts that a given
independent variable or other intervention
will not cause in some dependent measure.
• It is symbolically represented by H0
• H0 : as 𝝁c = 𝝁e
•

8. Alternative hypothesis
• The alternative hypothesis or experimental
hypothesis specifies that a difference exists
between the population parameters identified
by the null hypothesis. The alternative
hypothesis predicts that a given independent
variable or other intervention will cause in
some change in some dependent measure.
• It is represented as H1
• H1 :𝝁c ˃ 𝝁e

9. Rejection and Acceptance
• Anticipated relationship is found.
• Statisticians say we reject the null hypothesis
as false and accept the alternative hypothesis
as an adequate explanation for the time
being.
• An hypothesized relation H1 is not found
• We can accept or retain the null hypothesis.

10. A statistical Conclusion
• Any statistical conclusion is based exclusively
on the null hypothesis, which is either
accepted or rejected.

11. SIGNIFICANT TESTING
• A significant difference between group means
or averages, for example, is unlikely to occur
when population means are actually equal to
one another. Any significant difference, then,
suggests that each sample mean represents a
distinct and different population.
• Inference statistics rely heavily on this form of
significance testing

12. Significance testing
• Significance testing entails using statistical
tests and probabilities to determine whether
sample data can be used to accept or reject a
null hypothesis involving population
parameters.
• Statistical test is not synonymous to scientific
importance or the strength or size of a result.
A significant result is one that is reliable and
detectable through statistical means.

13. Probability or P Values
• An alternative term that is frequently used to
denote p value or significance level is alpha
level.
• Symbolized by Greek letter α

14. P Value
• The term p value, significance level, level of
significance, and alpha α level are generally
interchangeable.
• They all refer to some predetermined
probability level (e.g., .05, .01, .001) used to
assess the null hypothesis.