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Statistical Decision Making

Statistical Decision Making. History of the Student’s t Distribution and the t Test. Guinness and statistics. Hypothesis Testing. State the null hypothesis State the alternate hypothesis Select the level of significance Collect and summarize the sample data

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Statistical Decision Making

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  1. Statistical Decision Making

  2. History of the Student’s t Distribution and the t Test • Guinness and statistics

  3. Hypothesis Testing • State the null hypothesis • State the alternate hypothesis • Select the level of significance • Collect and summarize the sample data • Refer to the criterion for evaluating the sample evidence • Make a decision to discard/retain the null hypothesis

  4. Type I and Type II Errors

  5. Type I Measurement error Lack of random sample p value too liberal (p = .10) Investigator bias Improper use of one-tailed test Type II Measurement error Lack of sufficient power (N too small) P value too conservative (p = .01) Treatment effect not properly applied Possible Causes of Error

  6. The Alpha and p Levels • p value - probability with which the difference in means could occur by chance • Alpha () level - p value set prior to the experiment • Indication of risk willing to take in making a wrong decision to reject the null hypothesis • Smaller p values do not indicate greater importance of findings • Only indicates a smaller probability that the findings occurred by chance

  7. Two-Tailed Test • When direction of outcome is uncertain we use the null hypothesis • Ho is tested with a two-tailed test • If t does not reach p = .05, we know sample mean falls within the normal curve that includes 95% of all possible differences • Accept Ho with a 5% chance of being wrong • 5% rejection area divided between the 2 tails of the curve • Each area is 2.5% of the area under the curve

  8. One-Tailed Test • Use when direction of difference is know • Not sure what the size of difference is • Most likely trying to test H1 • Difference to be tested is always positive • Only use positive side of normal curve

  9. Why Use Statistical Decision Making? • Make decisions about differences between groups • Not necessarily that the 2 groups are different from each other • Did the two groups come from different populations?

  10. The t Test • Used when standard deviation of the population is not known • Need to calculate the standard error of the mean estimated from a sample • Using SEM we can determine odds that a sample is representative of the population it is drawn from

  11. The Independent t Test • Method comparing independent samples • Comparing means of 2 samples • Need to determine the standard error of the difference (SED) from the SEM of each sample • t Test becomes

  12. Independent t Test • Software packages • Calculate t value and p value • p typically = .05 as standard for rejecting null hypothesis • 5 times in 100

  13. Assumptions for the t Test • t Test produces reasonably reliable results • Robust measure • 4 assumptions • Population from which sample are drawn is normally distributed • Sample or samples are randomly selected from the population • Homogeneity of variance • Variance of one group should not be more than twice as large as the variance of the other • Data must be parametric • Interval or ratio measurement scale

  14. The Correlated t Test • Standard formulas for calculating t assume no correlation between groups • Dependent samples assume relationship (correlation) between scores from same group of subjects • Posttest is partially dependent on pretest score

  15. Correction for Correlated Samples • Need to make adjustment to denominator • T Test becomes

  16. Reading the Statistical Output • Figure 12-2 • Independent t Test • Figure 12-3 • Dependent t Test • Paired samples

  17. Statistical Power • Power - Ability of a test to correctly reject a false null hypothesis • Since critical t values are lower for one-tailed test, it is considered more powerful at a given p value • 1- is area of power

  18. Power • Power is dependent on 4 factors • Z level set by researcher • The difference between the 2 means being compared • The standard deviation of the 2 groups • Determines the spread of the curve • The sample size (N) of the 2 groups • Only N and Z are under your control

  19. Calculating Power • Power is calculated by determining Z, converting it to a percentile, and adding this percent to the 50% of the curve to the right of the experimental curve • t = Z + Z • Z = t - Z • Use table A to determine percentile for Z add that value to 50% • = 1-

  20. Sample Size • The only factor easily manipulated in power is N • How large does N need to be to produce a given power? • Complicated calculation • This is the last step

  21. Statistical vs. Clinical Significance • Which one is important? • Effect size holds the answer

  22. Effect Size • .30 is low • .50 is moderate • .80 is high • Should be obvious to clinician • Example from book • ES = 2.68/5.01 • ES = 0.53

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