2 Types of Inferential Statistics Parametric Statistics: estimate the value of a population parameter from the characteristics of a sampleAssumes the values in a sample are normally distributedInterval/Ratio level data requiredNonparametric Statistics:No assumptions about the underlying distribution of the sampleUsed when the data do not meet the assumption for a nonparametric test (ordinal and nominal data)
3 What are We Testing Anyway? Parametric Statistics: comparing the means of two or more groups relative to the variance within the groupsNonparametric Statistics: comparing the medians or ranks of two or more groupsTesting the null hypothesisStatistical Significance: determination that the differences between groups are large enough to be unlikely to have occurred by chance
4 Steps in the Test of Significance State the null hypothesis.State the alternative hypothesis.Set the level of significance associated with the null hypothesis (Type I Error).Select the appropriate test statistic.Compute the test statistic value.Determine the critical value needed for rejection of the null hypothesis for the particular statistic.Compare the obtained value to the critical value.Make a decision: Accept or reject the null hypothesis.
5 All These Tests! How do I know which one? The type of statistical test you use depends on several factors:Number of independent variablesNumber of levels of the independent variable(s)Number of dependent variablesIndependent vs. dependent samples (between vs. within groups design)Scale of measurement of the dependent variable
8 What Can We Conclude? Intact Groups Design (Quasi-Experiments) Subject Variables: conditions over which the experimenter has no direct controlCannot establish cause and effectCan only conclude that the groups are different from one anotherTrue ExperimentsManipulated Variables: conditions that the experimenter controls directly and to which he randomly assigns participantsAllows for cause and effect interpretations
9 The Power of a TestPower of a Test: the probability that one will reject H0 when it is a false statement. The power of a statistical analysis is represented as 1 – β.Reminder: β = the probability of making a Type II ErrorIt is influenced by:μX - μ0nσαType 2 error the probability of failing to reject a null hypothesis when it is false missed opportunityPower probability of NOT failing to reject the null when it is false the probability of accurately rejecting a false null hypothesis
10 Effect Size Statistics Due to the role of N (sample size) in the formulae for parametric statistics, a large sample size can make a negligible difference between groups appear significant.Because of this, current APA guidelines recommend computing effect size statistics in addition to parametric comparisons.
11 Uses of the Effect Size Statistic The effect size statistic can be used to:Estimate the true effect of the IVCompare the results of one research project to the results of other projectsEstimate the power of the statisticEstimate the number of subjects one needs in a research project to maximize the chance of rejecting a false hypothesis (power)