the argument for using statistics weighing the evidence statistical inference: an overview applying...
TRANSCRIPT
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?
The Argument for Using Statistics
Statistics are quantitative measurements of samples.
What do statistics tell us?
Weighing the Evidence
Descriptive statistics describe sample central tendency and variability.
Inferential statistics allow us to draw conclusions about a parent population from a sample.
What point does the Ms. Adams story make about evaluating experimental data?
Weighing the Evidence
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.
What point does the Ms. Adams story make about evaluating experimental data?
Weighing the Evidence
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.
Define sample and population.
Statistical Inference: An Overview
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.
What is statistical inference?
Statistical Inference: An Overview
Statistical inference is the process by which we make statements about a parent population based on a sample.
What does it mean when we conclude that our scores probably came from the same population?
Statistical Inference: An Overview
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.
What is variability?
Statistical Inference: An Overview
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.
What is variability?
Statistical Inference: An Overview
Which sample shown below has the most variability?
What is the null hypothesis?
Statistical Inference: An Overview
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.
What is statistical significance?
Statistical Inference: An Overview
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.
Explain the alternative hypothesis.
Statistical Inference: An Overview
The alternative hypothesis (H1) is the statement that the scores came from different populations the independent variable significantly affected the dependent variable.
When may we reject the null hypothesis?
Statistical Inference: An Overview
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.
What does a frequency distribution of scores reveal?
Statistical Inference: An Overview
The frequency distribution displays the number of individuals contributing a specific value of the dependent variable in a sample.
What does a frequency distribution of scores reveal?
Statistical Inference: An Overview
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.
Why does rejecting the null hypothesis depend on data variability?
Applying Statistical Inference: An Example
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.
Why does rejecting the null hypothesis depend on data variability?
Applying Statistical Inference: An Example
The greater the normal variability in the population, the larger the difference between groups required to reject the null hypothesis.
Contrast directional and nondirectional hypotheses.
Applying Statistical Inference: An Example
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.
Contrast directional and nondirectional hypotheses.
Applying Statistical Inference: An Example
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.
What is a significance level and how do we select one?
Applying Statistical Inference: An Example
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.
What is a significance level and how do we select one?
Applying Statistical Inference: An Example
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.
What are Type 1 and Type 2 errors?
Applying Statistical Inference: An Example
A Type 1 error () 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 () is accepting the null hypothesis when it is false.
How should we support null hypothesis testing?
Going Beyond Testing the Null Hypothesis
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).
How should we support null hypothesis testing?
Going Beyond Testing the Null Hypothesis
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.
How should we support null hypothesis testing?
Going Beyond Testing the Null Hypothesis
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).
What is a critical region?
The Odds of Finding Significance
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.
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