Chapter 9 Flashcards
Inferential Statistics
Statistical procedures designed to determine if differences and relationships found in sample data are sufficiently large that they can be assumed to be true at the population level
Degree of Uncertainty
All inferences from samples to populations involve a degree of uncertainty. The amount of uncertainty is determined by a number of factors, including sampling error and measurement error.
Measurement Error
This is differences in estimates of a population parameter based upon different testings of the same sample using the same instrument. These differences are the result of unreliability in our measurement instrument.
Sampling Error
This is the differences in estimates of a population parameter based upon different samples drawn from the same population. If the samples were randomly drawn and all of the same size, the amount of error (at a certain probability level) can be calculated.
Null Hypothesis
There is no difference between the groups (or the difference is in the unpredicted direction)
Alternative Hypothesis
There is a difference between the groups (or the difference is in the predicted direction)
level of significance
also known as a level
If the _____________ would have generated the sample statistic less often by chance than the a level, the researcher rejects the ______ and affirms the alternative.
null hypothesis, null
Type I Error
Rejecting the null when it is in fact true
Type II Error
Failing to reject the null when it is in fact false
Difference between group means
larger differences make it easier to achieve significance, all other things being equal
Sample size (N)
larger sample sizes reduce sampling error and make it easier to achieve significance, all other things being equal
Reliability of the instruments
more reliable instruments reduce measurement error, and make it easier to achieve significance, all other things being equal
Confidence Intervals
An interval within which we believe the true population parameter falls, at a given level of confidence (usually 95% or 99%)
Effect Size
Statistical significance answers the question, “Are the results likely to be due to sampling error?”
Sample size does not play a role in ______________.
effect size
Cohen’s d =
Mean One – Mean Two/Standard Deviation (Either Pooled or for Control)
Coefficient of Determination =
r squared (for correlations)
Eta Squared =
Sum of Squared Deviations Between/Sum of Squared Deviations Total
Parametric Statistics
Inferential statistical tests that make a number of assumptions about the data (normality, equality of group variances, and interval/ratio level of measurement)
Non-Parametric Statistics
Inferential statistical tests that make relatively few assumption about the data
Parametric statistics
are more “powerful” than non-parametric statistics; that is, they are more likely to reject the null hypothesis when it is in fact false
The t-test
Tests for differences between the means of two groups.
Independent samples t-test
Used to test differences in means of two different groups of subjects
Paired dependent samples t-test
Used to test differences in means of two groups of subjects who are either the same or matched on one or more variables
T-test for correlations
Tests whether a sample correlation is large enough to indicate a relationship different from zero in the population
Simple Analysis of Variance (One-Way ANOVA)
Tests for differences in the means of three or more groups representing levels of a single IV factor
Factorial Analysis of Variance (N-way ANOVA)
Allows testing of multiple IVs, each of which may have many levels.
Allows determination of the significance of each IV
Allows determination of the significance of changes in an IV as a function of changes in other IVs
Univariate
techniques have a single DV
Multivariate techniques
have multiple DVs
account for the correlations among the DVs (which would not happen if you ran multiple univariate tests)
Chi-Square
Used to analyze relationships among categorical variables
Appropriate when the DV is frequency of occurrence data (how many cases fall into each category or combination of categories)
Chi-square
is a non-parametric statistical test
Criteria for Evaluating Inferential Statistics
Basic descriptive statistics are needed to evaluate the results of inferential statistics
Inferential analyses refer to statistical, not practical significance
Inferential analyses do not indicate external validity (unless appropriate sampling was used in the design phase)
Inferential analyses do not indicate internal validity
The results of inferential tests depend on the number of subjects
The appropriate statistical test should be used
The level of significance should be interpreted correctly
Be wary of statistical tests with small numbers of subjects in one or more groups or categories
