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Choosing Statistical Procedures

Choosing Statistical Procedures. Types of Inferential Statistics. Parametric Statistics : estimate the value of a population parameter from the characteristics of a sample Assumes the values in a sample are normally distributed Interval/Ratio level data required Nonparametric Statistics :

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Choosing Statistical Procedures

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  1. Choosing Statistical Procedures

  2. Types of Inferential Statistics • Parametric Statistics: estimate the value of a population parameter from the characteristics of a sample • Assumes the values in a sample are normally distributed • Interval/Ratio level data required • Nonparametric Statistics: • No assumptions about the underlying distribution of the sample • Used 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 groups • Nonparametric Statistics: comparing the medians or ranks of two or more groups • Testing the null hypothesis • Statistical 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 variables • Number of levels of the independent variable(s) • Number of dependent variables • Independent vs. dependent samples (between vs. within groups design) • Scale of measurement of the dependent variable

  6. Selecting Statistical Tests

  7. What Can We Conclude? • Intact Groups Design (Quasi-Experiments) • Subject Variables: conditions over which the experimenter has no direct control • Cannot establish cause and effect • Can only conclude that the groups are different from one another • True Experiments • Manipulated Variables: conditions that the experimenter controls directly and to which he randomly assigns participants • Allows for cause and effect interpretations

  8. The Power of a Test • Power 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 Error • It is influenced by: • μX - μ0 • n • σ • α

  9. 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.

  10. Uses of the Effect Size Statistic • The effect size statistic can be used to: • Estimate the true effect of the IV • Compare the results of one research project to the results of other projects • Estimate the power of the statistic • Estimate the number of subjects one needs in a research project to maximize the chance of rejecting a false hypothesis (power)

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