Introduction to Statistics for the Social Sciences SBS200 - Lecture Section 001, Spring 2017 Room 150 Harvill Building 9:00 - 9:50 Mondays, Wednesdays & Fridays. Welcome http://www.youtube.com/watch?v=oSQJP40PcGI http://www.youtube.com/watch?v=oSQJP40PcGI

A note on doodling

Presentation Skills

Presentation Skills

Presentation Skills

Lab sessions Everyone will want to be enrolled in one of the lab sessions Project 2 Presentations

By the end of lecture today 3/6/17 Introduction to hypothesis testing Interpreting Alpha levels p values

Before next exam (April 7th) 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

Homework On class website: Please print and complete homework worksheet #17

No class on Friday Have a safe and happy spring break . Please note we DO have class on Wednesday 3/8

Some Mean Some Variability Construct a 95 percent confidence interval around the mean ? 95% ? raw score = mean ± (z score)(s.d.) Some Mean Some Variability We used this one when finding raw scores associated with an area under the curve. We had all population info. Not really a “confidence interval” because we know the mean of the population, so there is nothing to estimate or be “confident about”. Hint always draw a picture! We used this one when finding raw scores associated with an area under the curve. We used this to provide an interval within which we believe the mean falls. We have some level of confidence about our guess. We know the population standard deviation. raw score = mean ± (z score)(s.e.m.)

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

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

How do we know if something is going on 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?

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?

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

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 I’m not an outlier I just haven’t found my distribution yet If a score falls out into the tails (low probability) we conclude that it “must be” a common score from some other distribution

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

Rejecting the null hypothesis . null notnull big z score x x 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 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 . null x x small z score

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

How do we know how rare is rare enough? Area in the tails is alpha 99% α = .01 95% α = .05 90% α = .10 How do we know how rare is rare enough? Level of significance is called alpha (α) 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? 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”) 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

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 x2) 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

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

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 = 2.0? 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

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

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

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

90% Moving from descriptive stats into inferential stats…. For scores that fall into the middle range, we do not reject the null Moving from descriptive stats into inferential stats…. Critical z 1.64 Critical z -1.64 90% Measurements that occur within the middle part of the curve are ordinary (typical) and probably belong there 5% 5% Measurements that occur outside this middle ranges are suspicious, may be an error or belong elsewhere For scores that fall into the regions of rejection, we reject the null What percent of the distribution will fall in region of rejection Critical Values http://today.msnbc.msn.com/id/33411196/ns/today-today_health/ http://www.youtube.com/watch?v=0r7NXEWpheg

Thank you! See you next time!!