Chapter 7: Hypothesis Testing
Six steps involved:
1.
2.
3.
4.
5.
6.
State the null hypothesis (Ho)
State the alternative hypothesis (Ha)
Select a level of significance
Collect and summarize the sample data
Refer to a criterion for evaluating the sample evidence
Make a decision to discard/retain the null hypothesis
Step 1: State the Null Hypothesis (Ho)
A null hypothesis is a statement researchers make regarding the population
parameter. Usually stated in the following manner:
Ho: µ = 100
Ho: µmen = µwomen
Ho must deal with the population parameter(s), usually pinpoint in nature
(sometimes some researcher state as inexact).
Constraints of Ho


It must lie on the continuum of possible values
Cannot be fixed on the upper/lower limit of that continuum
Generally, researchers define the null hypothesis to be the exact of what their
hunches are; i.e. they then set up the research with the aim to prove that the null
hypothesis is false.
Step 2: State the Alternative Hypothesis (Ha)
An alternative hypothesis is a statement researchers make regarding the same
population parameter stated in Ho; stated in either a nondirectional or directional
fashion.
For example,
Ho: µ = 100
Ha: µ ≠ 100 (non directional, two-tailed test)
Or
Ha: µ > 100 (directional, one-tailed test)
Ho and Ha must be mutually exclusive. If the researcher rejects Ho, it means that
Ha could be true; and vice versa.
Step 3: Select a Level of Significance
The level of significance, alpha,  (usually set at .05), serves as a scientific cutoff
point that determines the decision concerning the null hypothesis.
To reject or fail-to-reject the null hypothesis, one of two possible comparisons is
made:
1. Compare the sample data’s calculated value with a critical value (which
is influenced by the choice of ). The critical value is determined from a
table of values influenced by . If calculated value is higher than the
critical value, the researcher will follow a decision to reject or fail-to-reject
Ho. The decision can be the calculated value is higher or lower than the
critical value (need not worry, it’s the researcher’s responsibility)
2. Compare the sample data’s p-value with the level of significance chosen,
i.e. . If p is less than , then Ho is rejected (e.g., p > .05).
Type I & Type II Errors
Type I Error:
Type II Error:
Rejecting a null hypothesis that is true
Accepting a null hypothesis that is false
The level of significance, , can be thought of as the probability of Type I Error,
i.e. rejecting a null hypothesis that is true. Hence, adjusting the level of
significance has an impact on the probability of committing a Type I Error, and
indirectly, affecting the probability of Type II Error as well. For example, if we set
 = 0.001 (or a very low number); it means we have a very small chance of
committing a Type I Error but conversely, the chances of committing a Type II
Error would become higher.
Step 4: Collect & Summarize Sample Data
Can be done with computers; to check with sample data are consistent with H o
A value, p, is usually included. This value refers to the probability that Ho is true
(cannot be rejected).
p is inversely proportional with the degree to which the sample data deviate from
Ho
Step 5: The Criterion for Evaluating the Sample Evidence
Using one of two criteria mentioned in Step 3 to evaluate sample evidence.
Step 6: Reject or Fail to reject Null Hypothesis
At the end of the hypothesis testing procedure, the researcher either:


Reject null hypothesis
Fail to reject null hypothesis
Many ways to describe rejecting null hypothesis:
 Ho was rejected
 A statistically significant finding was obtained
 A reliable difference was observed
 p is less than a small decimal value
Likewise, many ways to describe failure to reject null hypothesis:
 Ho was tenable, accepted
 No reliable differences were observed
 No significant differences were found
 p is greater than a small decimal value
Some Cautions about Hypothesis Testing
1.
When p is reported to be equal to or less than zero
Sometimes we may encounter research articles stating the sample data p
to be equal or less than zero. Recall that a small p causes Ho to be
rejected as it means that a true Ho population situation would not likely
produce a randomly selected data set like this. However, when p is stated
as equal to or less than zero, it does not mean that the imaginary
population defined by Ho has not chance of producing the obtained
sample data set!
The result of p being zero or less than zero is due to rounding off.
2.
Meaning of Significant in Research
In research study, when a sample data results is said to be significant, it
means the data obtained is inconsistent with the null hypothesis. Hence, it
is significant in the sense that the null hypothesis is rejected. It does not
mean that the results or findings of the research are significant (in the
traditional sense of the word). That would depend on the research
question, design of research etc.