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Understanding Type I and Type II Errors, Effect Size, and Statistical Power in Inferential Statistics

This guide delves into the concepts of Type I and Type II errors in inferential statistics. Type I errors occur when the null hypothesis (H0) is incorrectly rejected when it is true, while Type II errors happen when H0 is accepted when it is false. We also explore statistical power, which measures the probability of correctly rejecting H0 when it is false, and how effect size quantifies the strength of a phenomenon. Key factors affecting power include alpha levels, sample size, and variance, emphasizing the importance of statistical considerations in research design.

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Understanding Type I and Type II Errors, Effect Size, and Statistical Power in 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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