The Argument for Using Statistics
Weighing the Evidence
Statistical Inference: An Overview
Applying Statistical Inference: An Example
Going Beyond Testing the Null Hypothesis
The Odds of Finding Significance
Test Statistics
Organizing and Summarizing Data
What are statistics?
Statistics are quantitative measurements of
samples.
The Argument for Using Statistics
What do statistics tell us?
Descriptive statistics describe sample central
tendency and variability.
Inferential statistics allow us to draw
conclusions about a parent population from a
sample.
Weighing the Evidence
What point does the Ms. Adams story make about
evaluating experimental data?
Just as Detective Katz can at best show that
Ms. Adams is probably guilty, in statistics
we can only state that the independent variable
probably affected the dependent variable.
Weighing the Evidence
What point does the Ms. Adams story make about
evaluating experimental data?
While we cannot prove that the independent
variable definitely caused the change in the
dependent variable, we can state the probability
that our conclusion is correct.
Weighing the Evidence
Define sample and population.
A population is a set of people, animals, or
objects that share at least one characteristic
in common (like college sophomores).
A sample is a subset of the population that we
use to draw inferences about the population.
Statistical Inference: An Overview
What is statistical inference?
Statistical inference is the process by which
we make statements about a parent population
based on a sample.
Statistical Inference: An Overview
What does it mean when we conclude that our
scores probably came from the same population?
The differences in scores obtained from separate
treatment groups are not significantly greater
than what we might expect between any
samples randomly drawn from this population.
When researchers report this outcome, it means
that were was no treatment effect.
Statistical Inference: An Overview
What is variability?
For a set of dependent variable measurements,
there is variability when the scores are different.
Variability “spreads out” a sample of scores
drawn from a population.
Statistical Inference: An Overview
What is variability?
Which sample shown below has the most variability?
Statistical Inference: An Overview
What is the null hypothesis?
The null hypothesis (H0) is the statement that
the scores came from the same population and
the independent variable did not significantly
affect the dependent variable.
Statistical Inference: An Overview
What is statistical significance?
Results are statistically significant when
the difference between our treatment groups
exceeds the normal variability of scores on
the dependent variable.
Statistical significance means that there is a
treatment effect at an alpha level we have
preselected, like .01 or .05.
Statistical Inference: An Overview
Explain the alternative hypothesis.
The alternative hypothesis (H1) is the
statement that the scores came from different
populations the independent variable
significantly affected the dependent variable.
Statistical Inference: An Overview
When may we reject the null hypothesis?
We may reject the null hypothesis when the
differences between treatment groups exceed
the normal variability in the dependent variable
at our chosen level of significance.
Statistical Inference: An Overview
What does a frequency distribution of scores reveal?
The frequency distribution displays the
number of individuals contributing a specific
value of the dependent variable in a sample.
Statistical Inference: An Overview
What does a frequency distribution of scores reveal?
The values of the dependent variable are
indicated on the horizontal X-axis (abscissa)
and the frequencies of these values are
indicated on the vertical Y-axis (ordinate).
You can calculate the total number of
participants by adding the frequencies.
Statistical Inference: An Overview
Why does rejecting the null hypothesis depend on
data variability?
The decision to accept or reject the null
hypothesis depends on whether the differences
we measure between treatment groups are
significantly greater than the normal variability
among people in the population.
Applying Statistical Inference: An Example
Why does rejecting the null hypothesis depend on
data variability?
The greater the normal variability in the
population, the larger the difference between
groups required to reject the null hypothesis.
Applying Statistical Inference: An Example
Contrast directional and nondirectional hypotheses.
A directional hypothesis predicts the “direction”
of the difference between two groups on the
dependent variable.
For example: The experimental group will lower
their systolic blood pressure more than the
control group.
Applying Statistical Inference: An Example
Contrast directional and nondirectional hypotheses.
A nondirectional hypothesis predicts that the
two groups will have different values on the
dependent variable:
For example: The experimental group and
control group will achieve different systolic blood
pressure reductions.
Applying Statistical Inference: An Example
What is a significance level and how do we select
one?
The significance level (alpha) is our criterion
for deciding whether to accept or reject the null
hypothesis.
Psychologists do not use a significance level
larger than .05.
Applying Statistical Inference: An Example
What is a significance level and how do we select
one?
A significance level of .05 means that a pattern
of results is so unlikely that it could have
occurred by chance fewer than 5 times out of
100.
Applying Statistical Inference: An Example
What are Type 1 and Type 2 errors?
A Type 1 error (a) is rejecting the null
hypothesis when it is correct. The experimenter
determines the risk of a Type 1 error by selecting
the alpha level.
A Type 2 error (b) is accepting the null
hypothesis when it is false.
Applying Statistical Inference: An Example
How should we support null hypothesis testing?
An American Psychological Association task
force recommended that researchers include
estimates of effect size and confidence intervals,
in addition to p values.
When you calculate a p value that is statistically
significant, this means that your results are
unlikely to be due to chance (are probably real).
Going Beyond Testing the Null Hypothesis
How should we support null hypothesis testing?
Effect size estimates the strength of the
association between the independent and
dependent variable—the percentage of the
variability in the dependent variable is due
to the independent variable.
Going Beyond Testing the Null Hypothesis
How should we support null hypothesis testing?
A confidence interval is a range of values
above and below a sample mean that is likely
to contain the population mean (usually 95%
or 99% of the time).
Going Beyond Testing the Null Hypothesis
What is a critical region?
A critical region is a region of the distribution
of a test statistic sufficiently extreme to reject
the null hypothesis.
For example, if our criterion is the .05 level, the
critical region consists of the most extreme 5%
of the distribution.
The Odds of Finding Significance
What is a critical region?
To reject the null hypothesis, the test statistic
would have to fall within the shaded critical
region.
The Odds of Finding Significance
What are one-tailed and two-tailed tests?
A one-tailed test has a critical region at one tail
of the distribution. We use a one-tailed test with
a directional hypothesis.
A two-tailed test has two critical regions, found
at opposite ends of the distribution. We use a
two-tailed test with a nondirectional hypothesis.
The Odds of Finding Significance
What is the function of inferential statistics?
Inferential statistics allow us to predict the
behavior of a population from a sample.
Examples of inferential statistics are the t test
and F test.
Test Statistics