Interpreting NonSignificant Results
Prerequisites
Introduction
to Hypothesis Testing, Significance
Testing , Type
I and II Errors
Learning Objectives
 State what it means to accept the null hypothesis
 Explain why the null hypothesis should not be accepted
 Describe how a nonsignificant result can increase confidence that
the null hypothesis is false
 Discuss the problems of affirming a negative conclusion
When a significance test results in a high probability
value, it means that the data provide no evidence that the null
hypothesis is false. However, the high probability value is not
evidence that the null hypothesis is true.
Concluding that the null hypothesis is true is
called accepting the null hypothesis.
To do so is a serious error.
Binomial
Calculator
Further argument for not accepting the null hypothesis
Do not accept the null hypothesis when you do
not reject it.
So how should the nonsignificant result be interpreted?
What if I claimed to have been Socrates in an earlier life? Since
I have no evidence for this claim, I would have great difficulty
convincing anyone that it is true. However, no one would be able
to prove definitively that I was not.
Although there is never a statistical basis for
concluding that an effect is exactly zero, a statistical analysis
can demonstrate that an effect is at most small. This is done
by computing a confidence interval.
If all effect sizes in the interval are small, then it can be
concluded that the effect is small.
