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Chapter 3

Chapter 3. Normal Curve, Probability, and Population Versus Sample Part 2 Tues. Sept. 3, 2013. Using the Table: From % back to Z or raw scores. Steps for figuring Z scores and raw scores from percentages:

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Chapter 3

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  1. Chapter 3 Normal Curve, Probability, and Population Versus Sample Part 2 Tues. Sept. 3, 2013

  2. Using the Table: From % back to Z or raw scores • Steps for figuring Z scores and raw scores from percentages: 1. Draw normal curve, shade in approximate area for the % (using the 50%-34%-14% rule) 2. Make rough estimate of the Z score where the shaded area starts 3. Find the exact Z score using the normal curve table: • look up the % and find its z score (see example)

  3. (cont.) 4. Check that your Z score is similar to the rough estimate from Step 2 5. If you want to find a raw score, change it from the Z score, using formula: x = Z(SDx) + Mx

  4. Probability • Probability • Expected relative frequency of a particular outcome • Outcome • The result of an experiment

  5. Probability • Range of probabilities • Probabilities as symbols • p • p < .05 (probability is less than .05) • Probability and the normal distribution • Normal distribution as a probability distribution • Probability of scoring betw M and +1 SD = .34 (In ND, 34% of scores fall here)

  6. Sample and Population • Population parameters and sample statistics– note the different notation for pop or sample • M for sample is  for population • SD for sample is  for population

  7. Ch 4 – Intro to Hypothesis Testing Part 1

  8. Hypothesis Testing • Procedure for deciding whether the outcome of a study support a particular theory • Logic: • Considers the probability that the result of a study could have come about if the experimental procedure had no effect • If this probability is low, scenario of no effect is rejected and the theory is supported

  9. The Hypothesis Testing Process • Restate the question as a research hypothesis & a null hypothesis • Research hypothesis –supports your theory. • Example? • Null hypothesis – opposite of research hyp; no effect (no group differences). This is tested. • Example?

  10. The Hypothesis Testing Process • Determine the characteristics of the comparison distribution • Comparison distribution – what the distribution will look like if the null hyp is true. • Example? Note – we recognize there will be sampling errors in our sample mean

  11. The Hypothesis Testing Process • Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected • Cutoff sample score (critical value) – how extreme a difference do we need to reject the null hyp? • Conventional levels of significance: p < .05, p < .01 • We reject the null if probability of getting a result that extreme is .05 (or .01…)

  12. Step 3 (cont.) • How do we find this critical value? • Use conventional levels of significance: p < .05, p < .01 • Find the z score from Appendix Table 1 if 5% in tail of distribution (or 1%) For 5%  z = 1.64 • We reject the null if probability of getting a result that extreme is .05 (or .01…) • Reject the null hyp if my sample z > 1.64 • What does it mean to reject the null at .05 alpha level?

  13. The Hypothesis Testing Process • Determine your person’s score on the comparison distribution • Collect data, calculate the z score for your person of interest • Use comparison distribution – how extreme is that score? • Decide whether to reject the null hypothesis • If your z score of interest falls within critical/rejection region  Reject Null. (If not, fail to reject the null) • Rejecting null hypothesis means there is support for research hypothesis. • Example?

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