1 / 24

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?.

roman
Download Presentation

EDL 7150 Inferential Statistics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related