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EDL 7150 Inferential Statistics

EDL 7150 Inferential Statistics. Type I and Type II Errors, Effect Size andStatistical Power. Type I and Type II Errors What happens when we Accept H 0 when it is True ? Have we made and error?.

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EDL 7150 Inferential Statistics

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  1. EDL 7150Inferential Statistics Type I and Type II Errors, Effect Size andStatistical Power

  2. Type I and Type II ErrorsWhat happens when we Accept H0 when it is True? Have we made and error?

  3. Type I and Type II ErrorsWhat happens when we Accept H0 when it is True?Have we made and error?

  4. Type I and Type II ErrorsWhat happens when we Accept H0 when it is True? Have we made and error?

  5. Type I and Type II ErrorsWhat happens when we Reject H0 when it is False? Have we made and error?

  6. Type I and Type II ErrorsWhat happens when we Reject H0 when it is False? Have we made and error?

  7. Type I and Type II ErrorsWhat happens when we Reject H0 when it is False? Have we made and error?

  8. Type I and Type II ErrorsWhat happens when we Reject H0 when it is True? Have we made and error?

  9. Type I and Type II ErrorsWhat happens when we Reject H0 when it is True? Have we made and error?

  10. Type I and Type II ErrorsWhat happens when we Reject H0 when it is True? Have we made and error?

  11. Type I and Type II ErrorsWhat happens when we Reject H0 when it is True? Have we made and error?

  12. Type I and Type II Errors • When a TRUE null hypothesis is REJECTED a TYPE I Error has been made. • The probability of a TYPE I Error is  (alpha). • Set by the researcher. • The risk (probability) of being wrong. • Probabilities of .05 and .01 are conventional.

  13. Type I and Type II ErrorsWhat happens when we Accept H0 when it is False? Have we made and error?

  14. Type I and Type II ErrorsWhat happens when we Accept H0 when it is False? Have we made and error?

  15. Type I and Type II ErrorsWhat happens when we Accept H0 when it is False? Have we made and error?

  16. Type I and Type II ErrorsWhat happens when we Accept H0 when it is False? Have we made and error?

  17. Type I and Type II Errors • When a FALSE null hypothesis is ACCEPTED (or, better, RETAINED) a TYPE II Error has been committed. • The probability of a TYPE II Error is β (beta). • We usually do not know β, but we can estimate it. • We are more interested in (1- β), or power.

  18. Statistical Power • Statistical power (1-β) is the probability of REJECTING of H0 when it is FALSE. • This is the objective • Power is the probability of avoiding a TYPE II Error • Several factors affect power: • The alpha level. • Sample size. • Sample variance. • Magnitude of the effect (typically µ1 - µ2). • Statistical procedure used.

  19. Effect Size • Of the factors that affect power, magnitude of the effect plays a central role in computing effect sizes. • The most common equation for computing an effect size is given by Δ, where:

  20. Effect Size: An example • Suppose we are comparing two methods of teaching Algebra: One using a Saxon text and one using a traditional, Holt, say, text. • Scores on a standardized Algebra test, following the intervention are MSaxon = 38 and MTraditonal = 32. • There corresponding standard deviations are SDSaxon = 8 and SDTraditonal =10, respectively. • There are 19 students in the Saxon group and 22 students in the traditional group.

  21. Effect Size: An example (Continued) • First, compute: t = (MSaxon-MTraditonal)/SEDiff = (38 – 32) / 2.884 = 2.08 With (n1+n2-2) = 39 degrees of freedom. • Hence, we have, using a statistical phrase, t(39) = 2.08; p < .05. • What was the effect size?

  22. Effect Size: An example (Continued) • Since the t test is significant we can estimate the effect size: • Since we are estimating, substitute d for Δ, MSasxon and MTraditional for µsaxon and µtraditonal and SDTraditonal for σ. • Hence, d = (38-32)/10 = .60.

  23. Effect Size: An example (Continued • So the effect size (d) is .6. What does this mean. • Notice that in calculating the effect size the denominator was the standard deviation of the Traditional group (the control group, in this case). • So, the effect size shows how far the Saxon group scored above the Traditional group in standard deviation units. • In a table of the normal distribution it can be seen that an effect size of .6 is at the 73ed %tile.

  24. Interpreting Effect Sizes • Coehen (1988) proposed some conventions for interpreting effect sizes, that have more or less been followed in the literature. Small effect size: .20 Moderate effect size: .50 Large effect size: .80

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