Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Spring 2019 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays & Fridays. March 13 http://www.youtube.com/watch?v=oSQJP40PcGI

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Before next exam (April 5th) Schedule of readings Before next exam (April 5th) Please read chapters 1 - 11 in OpenStax textbook Please read Chapters 2, 3, and 4 in Plous Chapter 2: Cognitive Dissonance Chapter 3: Memory and Hindsight Bias Chapter 4: Context Dependence

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Rejecting the null hypothesis The result is “statistically significant” if: the observed statistic is larger than the critical statistic observed stat > critical stat If we want to reject the null, we want our t (or z or r or F or x2) 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 Review

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

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

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

One versus two tail test of significance: Comparing different critical scores (but same alpha level – e.g. alpha = 5%) 1.64 95% 5% 95% z score = -1.64 reject null 2.5% 2.5% 95% How would the critical z change? Critical scores get smaller with one tailed test 5% One tail test requires: 1. a unidirectional prediction (predict which group will have larger mean) and 2. that the results actually be in the predicted direction (predicted mean is larger) So, in a one-tailed test the “region of rejection” refers to results in the predicted direction If results are NOT in predicted direction, it is impossible to reject the null Review

One versus two tail test of significance 5% versus 1% alpha levels How would the critical z change? One-tailed Two-tailed α = 0.05 Significance level = .05 α = 0.01 Significance level = .01 1% 5% 2.5% .5% .5% 2.5% -1.64 or +1.64 -1.96 or +1.96 -2.33 or +2.33 -2.58 or +2.58 Review

One versus two tail test of significance 5% versus 1% alpha levels What if our observed z = 2.0? How would the critical z change? One-tailed Two-tailed α = 0.05 Significance level = .05 α = 0.01 Significance level = .01 -1.64 or +1.64 -1.96 or +1.96 Remember, reject the null if the observed z is bigger than the critical z Reject the null Reject the null -2.33 or +2.33 -2.58 or +2.58 Do not Reject the null Do not Reject the null Review

One versus two tail test of significance 5% versus 1% alpha levels What if our observed z = 1.75? How would the critical z change? One-tailed Two-tailed α = 0.05 Significance level = .05 α = 0.01 Significance level = .01 -1.64 or +1.64 -1.96 or +1.96 Remember, reject the null if the observed z is bigger than the critical z Do not Reject the null Reject the null -2.33 or +2.33 -2.58 or +2.58 Do not Reject the null Do not Reject the null Review

One versus two tail test of significance 5% versus 1% alpha levels What if our observed z = 2.45? How would the critical z change? One-tailed Two-tailed α = 0.05 Significance level = .05 α = 0.01 Significance level = .01 -1.64 or +1.64 -1.96 or +1.96 Remember, reject the null if the observed z is bigger than the critical z Reject the null Reject the null -2.33 or +2.33 -2.58 or +2.58 Reject the null Do not Reject the null Review

One versus two tail test of significance 5% versus 1% alpha levels What if our observed z = 2.45? How would the critical z change? Which situation (alpha and tail) would make it easiest to reject the null? One-tailed Two-tailed α = 0.05 Significance level = .05 α = 0.01 Significance level = .01 why? -1.64 or +1.64 -1.96 or +1.96 Remember, reject the null if the observed z is bigger than the critical z Reject the null Reject the null -2.33 or +2.33 -2.58 or +2.58 Reject the null Do not Reject the null Review

Two tail tests One tail tests Review In a one-tailed test do we use a negative or positive z score? Doesn’t matter whether the z is positive or negative If prediction was right, reject the null if observed score is larger than the critical score Two tail tests But, if prediction was wrong, it is impossible to reject the null anyway One tail tests Which type of test REQUIRES that you make a prediction about which group mean will be larger? When we go from the regular two-tailed test to a one tail test, what happens to the critical z? Only the one-tail test does So, if prediction was right, it is easier to reject the null The critical score get smaller But, if prediction was wrong, it is impossible to reject the null So, if prediction was right, it is easier to reject the null But, if prediction was wrong, it is impossible to reject the null Review

Whether or not feed had corn oil No, feed had no corn oil Yes, the feed had corn oil Weight of eggs There is no difference in the weight of eggs based on corn oil in food There is a difference in the weight of eggs based on corn oil in food This is a two-tailed test (no prediction was made) true experiment between nominal ratio 1.96

Yes Yes Yes Yes 2.58 No No No No The weights of eggs for chickens who received the corn oil was 63 grams, while the weights of the eggs for chickens who did not receive the corn oil was 60 grams. A z-test found this to be a significant difference z = 2.42; p < 0.05

Whether or not offered incentive Was offered incentive Was not offered incentive Grade point average There is no difference in GPA based on level of incentive There is a difference in GPA based on level of incentive This is a two-tailed test (no prediction was made) true experiment between nominal interval 1.96

Yes Yes Yes Yes 2.58 Yes Yes Yes Yes The average GPA was 2.3 for students who were offered an incentive and was 2.1 for students who were not offered an incentive. A z-test was completed and we found this to be a significant difference z = 3.64; p < 0.05

Whether or not video included sound Video with no sound Video with sound Number of items correctly recalled There is no difference in the number of items recalled There is a difference in the number of items recalled This is a two-tailed test (no prediction was made) true experiment between nominal ratio 1.96

No No No No 2.58 No No No No The average number of items recalled was 3.7 for the students who watched the ads with no sound, and was 3.3 for students who watched video with sound. A z-test was completed and we found no significant difference z = 1.17; n.s.

Location of air conditioner plant Japan United States Turnover rate There is no difference in the turnover rates between Japan and USA There is no difference in the turnover rates between Japan and USA This is a two-tailed test (no prediction was made) quasi between nominal ratio 1.96

Yes Yes Yes Yes 2.58 Yes Yes Yes Yes The average turnover rate in the Japanese plants is 3.12 while the average turnover rated in the American plants is 6.56. A z-test showed a significant difference, z = -4.46; p < 0.05

Thank you! See you next time!!