2. Introduction to Statistics for the Social Sciences SBS200, COMM200, GEOG200, PA200, POL200, or SOC200 Lecture Section 001, Spring 2015 Room 150 Harvill Building 8:00 - 8:50 Mondays, Wednesdays & Fridays.

4. Schedule of readings Before next exam (April 10 th ) Please read chapters 7 – 11 in Ha & Ha Please read Chapters 2, 3, and 4 in Plous Chapter 2: Cognitive Dissonance Chapter 3: Memory and Hindsight Bias Chapter 4: Context Dependence

5. By the end of lecture today 3/23/15 Use this as your study guide Logic of hypothesis testing Steps for hypothesis testing Levels of significance (Levels of alpha) what does p < 0.05 mean? what does p < 0.01 mean?

6. Labs continue this week Project 2

7. Create example of t-test Identify single IV (two levels) Identify DV (must be numeric) Graph should have two bars (one for each mean) Think about how you might Study Type 2: t-test Comparing Two Means? Use a t-test t-test: Curly vs Straight hair

13. Confidence Interval of 99% Has and alpha of 1% α =.01 Confidence Interval of 90% Has and alpha of 10% α =. 10 Confidence Interval of 95% Has and alpha of 5% α =.05 99%95%90% Area outside confidence interval is alpha Area in the tails is called alpha Area associated with most extreme scores is called alpha Critical z -2.58 Critical z 2.58 Critical z -1.96 Critical z 1.96 Critical z -1.64 Critical z 1.64

14. Moving from descriptive stats into inferential stats…. Measurements that occur outside this middle ranges are suspicious, may be an error or belong elsewhere Measurements that occur within the middle part of the curve are ordinary (typical) and probably belong there 99%95%90% Area outside confidence interval is alpha

15. How do we know if something is going on? How rare/weird is rare/weird enough? Every day examples about when is weird, weird enough to think something is going on? Handing in blue versus white test forms Psychic friend – guesses 999 out of 1000 coin tosses right Cancer clusters – how many cases before investigation Weight gain treatment – one group gained an average of 1 pound more than other group…what if 10?

16. Why do we care about the z scores that define the middle 95% of the curve? Inferential Statistics Hypothesis testing with z scores allows us to make inferences about whether the sample mean is consistent with the known population mean. Is the mean of my observed sample consistent with the known population mean or did it come from some other distribution?

17. Why do we care about the z scores that define the middle 95% of the curve? If the z score falls outside the middle 95% of the curve, it must be from some other distribution If a score falls out into the 5% range we conclude that it “must be” actually a common score but from some other distribution Main assumption: We assume that weird, or unusual or rare things don’t happen That’s why we care about the z scores that define the middle 95% of the curve

18. . I’m not an outlier I just haven’t found my distribution yet Main assumption: We assume that weird, or unusual or rare things don’t happen If a score falls out into the tails (low probability) we conclude that it “must be” a common score from some other distribution

19. ... 95% X Relative to this distribution I am unusual maybe even an outlier Relative to this distribution I am utterly typical Reject the null hypothesis Support for alternative hypothesis X

20. . Rejecting the null hypothesis If the observed z falls beyond the critical z in the distribution (curve): then it is so rare, we conclude it must be from some other distribution then we reject the null hypothesis then we have support for our alternative hypothesis If the observed z falls within the critical z in the distribution (curve): then we know it is a common score and is likely to be part of this distribution, we conclude it must be from this distribution then we do not reject the null hypothesis then we do not have support for our alternative not null x null big z score Alternative Hypothesis. x null small z score x x

21. Rejecting the null hypothesis If the observed z falls beyond the critical z in the distribution (curve): then it is so rare, we conclude it must be from some other distribution then we reject the null hypothesis then we have support for our alternative hypothesis If the observed z falls within the critical z in the distribution (curve): then we know it is a common score and is likely to be part of this distribution, we conclude it must be from this distribution then we do not reject the null hypothesis then we do not have support for our alternative hypothesis

22. How do we know how rare is rare enough? Critical z: A z score that separates common from rare outcomes and hence dictates whether the null hypothesis should be retained (same logic will hold for “critical t”) The degree of rarity required for an observed outcome to be “weird enough” to reject the null hypothesis Which alpha level would be associated with most “weird” or rare scores? Level of significance is called alpha ( α ) If the observed z falls beyond the critical z in the distribution (curve) then it is so rare, we conclude it must be from some other distribution 99%95%90% α =.01 α =.05 α =.10 Area in the tails is alpha

23. Rejecting the null hypothesis The result is “statistically significant” if: the observed statistic is larger than the critical statistic (which can be a ‘z” or “t” or “r” or “F” or x 2 ) observed stat > critical stat If we want to reject the null, we want our t (or z or r or F or x 2 ) to be big!! the p value is less than 0.05 (which is our alpha) p < 0.05 If we want to reject the null, we want our “p” to be small!! we reject the null hypothesis then we have support for our alternative hypothesis

24. Confidence Interval of 99% Has and alpha of 1% α =.01 Confidence Interval of 90% Has and alpha of 10% α =. 10 Confidence Interval of 95% Has and alpha of 5% α =.05 99%95%90% Critical z -2.58 Area in the tails is called alpha Critical z 2.58 Critical z -1.96 Critical z 1.96 Critical z -1.64 Critical z 1.64 Critical Z separates rare from common scores

25. How would the critical z change? α = 0.05 Significance level =.05 α = 0.01 Significance level =.01 -1.96 or +1.96 -2.58 or +2.58 What if our observed z = 2.0? Reject the null Do not Reject the null Remember, reject the null if the observed z is bigger than the critical z Deciding whether or not to reject the null hypothesis.05 versus.01 alpha levels p < 0.05 Yes, Significant difference Not a Significant difference

26. How would the critical z change? α = 0.05 Significance level =.05 α = 0.01 Significance level =.01 -1.96 or +1.96 -2.58 or +2.58 What if our observed z = 1.5? Do Not Reject the null Do Not Reject the null Remember, reject the null if the observed z is bigger than the critical z Deciding whether or not to reject the null hypothesis.05 versus.01 alpha levels Not a Significant difference

27. How would the critical z change? α = 0.05 Significance level =.05 α = 0.01 Significance level =.01 -1.96 or +1.96 -2.58 or +2.58 What if our observed z = -3.9? Reject the null Remember, reject the null if the observed z is bigger than the critical z Deciding whether or not to reject the null hypothesis.05 versus.01 alpha levels p < 0.05 Yes, Significant difference p < 0.01 Yes, Significant difference

28. How would the critical z change? α = 0.05 Significance level =.05 α = 0.01 Significance level =.01 -1.96 or +1.96 -2.58 or +2.58 What if our observed z = -2.52? Reject the null Do not Reject the null Remember, reject the null if the observed z is bigger than the critical z Deciding whether or not to reject the null hypothesis.05 versus.01 alpha levels p < 0.05 Yes, Significant difference Not a Significant difference