Transcript Slide 1
Part IV
Significantly Different:
Using Inferential Statistics
Chapter 9
Significantly Significant:
What it Means for You and Me
The Concept of Significance
Any difference between groups that is due to
a systematic influence rather than chance
Must assume that all other factors that might
contribute to differences are controlled
If Only We Were Perfect…
Significance level
The risk associated with not being absolutely
sure that what occurred in the experiment is a
result of what you did or what is being tested
The goal is to eliminate competing reasons
for differences as much as possible.
Statistical Significance
The degree of risk you are willing to take that
you will reject a null hypothesis when it is
actually true.
The World’s Most Important Table
Type I Errors (Level of Significance)
The probability of rejecting a null hypothesis
when it is true
Represented by alpha ( )
Conventional levels are set between .01
and .05
Choice of alpha often depends on the
consequences of being wrong
Type II Errors
The probability of accepting a null hypothesis
when it is false
Referred to as “Beta”
Represented by β
Power = 1- β
Significance Versus Meaningfulness
A finding can be statistically significant but
not very meaningful
A finding can be statistically significant but
not “big enough”
Statistical significance should not be the only
goal of scientific research
Effect Size
Significance is influenced by sample size and
variability…we’ll talk more about this later.
How Inference Works
A representative sample of the population is
chosen.
Data is collected, a mean (or means) are
computed and compared to population
means (real or hypothesized)
A conclusion is reached as to whether the
mean is statistically significant (i.e. different
from the population mean)
Based on the results of the sample, an
inference is made about the population.
Deciding What Test to Use
Tests of Significance – A General Process
1. A statement of the null hypothesis.
2. Set the level of risk associated with the null
hypothesis. (alpha)
3. Select the appropriate test statistic.
4. Compute the test statistic (obtained) value
5. Determine the value needed to reject the null
hypothesis using the appropriate table of critical
values
6. Compare the obtained value to the critical
value
7. If obtained value is more extreme, reject the null
hypothesis
8. If obtained value is not more extreme, accept
the null hypothesis
The Picture Worth a Thousand Words