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BHS 204-01 Methods in Behavioral Sciences I

BHS 204-01 Methods in Behavioral Sciences I. April 25, 2003 Chapter 6 (Ray) The Logic of Hypothesis Testing. Degrees of Freedom. Degrees of freedom (df) – how many numbers can vary and still produce the observed result. Population statistics include the degrees of freedom.

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BHS 204-01 Methods in Behavioral Sciences I

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  1. BHS 204-01Methods in Behavioral Sciences I April 25, 2003 Chapter 6 (Ray) The Logic of Hypothesis Testing

  2. Degrees of Freedom • Degrees of freedom (df) – how many numbers can vary and still produce the observed result. • Population statistics include the degrees of freedom. • Calculated differently depending upon the experimental design – based on the number of groups. • T-Test df = (Ngroup1 -1) + (Ngroup2 -1)

  3. Reporting T-Test Results • Include a sentence that gives the direction of the result, the means, and the t-test results. • Example: • The experimental group showed significantly greater weight gain (M = 55) compared to the control group (M = 21), t(12) = 3.97, p=.0019, two-tailed. • Give the exact probability of the t value. • Underline all statistics.

  4. When to Use a T-Test • When two independent groups are compared. • When sample sizes are small (N< 30). • When the actual population distribution is unknown (not known to be normal). • When the variances within the two groups are unequal. • When sample sizes are unequal.

  5. Using Error Bars in Graphs • Error bars show the standard error of the mean for the observed results. • To visually assess statistical significance, see whether: • The mean (center point of error bar) for one group falls outside the error bars for the other group. • Also compare how large the error bars are for the two groups.

  6. Figure 5.8. (p. 124)Graphic illustration of cereal experiment.

  7. Sources of Variance • Systematic variation – differences related to the experimental manipulation. • Can also be differences related to uncontrolled variables (confounds) or systematic bias (e.g. faulty equipment or procedures). • Chance variation – nonsystematic differences. • Cannot be attributed to any factor. • Also called “error”.

  8. F-Ratio • A comparison of the differences between groups with the differences within groups. • Between-group variance = treatment effect + chance variance. • Within-group variance = chance variance. • If there is a treatment effect, then the between-group variance should be greater than the within-group variance.

  9. Testing the Null Hypothesis • Between-group variance (treatment effect) must be greater than within-group variance (chance variation), F > 1.0. • How much greater? • Normal curve shows that 2 SD, p <.05 is likely to be a meaningful difference. • The p value is a compromise between the likelihood of accepting a false finding and the likelihood of not accepting a true hypothesis.

  10. Box 6.1. (p. 135)Type I and Type II Errors.

  11. Type I error – likelihood of rejecting the null when it is true and accepting the alternative when it is false (making a false claim). • This is the p value -- .05 is probability of making a Type I error. • Type II error – likelihood of accepting null when it is false and rejecting the alternative when it is true. • Probability is b, the power of a statistic is 1-b.

  12. Reporting the F-Ratio • ANOVA is used to calculate the F-Ratio. • Example: • The experimental group showed significantly greater weight gain (M = 55) compared to the control group (M = 21), F(1, 12) = 4.75, p=.05. • Give the degrees of freedom for the numerator and denominator.

  13. When to Use ANOVA • When there are two or more independent groups. • When the population is likely to be normally distributed. • When variance is similar within the groups compared. • When group sizes (N’s) are close to equal.

  14. Threats to Internal Validity • It is the experimenter’s job to eliminate as many threats to internal validity as possible. • Such threats constitute sources of systematic variance that can be confused with an effect, resulting in a Type I error. • Potential threats to validity must be evaluated in the Discussion section of the research report.

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