KIN 4310 1nd Edition Lecture 10 Outline of Last Lecture I Section 2 Topics II What is The Truth III Validity IV Validity The Idea V Validity VI Content Validity VII Criterion Validity VIII Predictive Concurrent Validity IX Construct Validity X Reliability XI Validity XII Example XIII Validity and Reliability XIV Take home Messages XV Reliability and Validity Outline of Current Lecture I Definition II Z Scores These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute III Interpreting Z Scores IV Normal Distribution V Z Score Formulas VI Example Male Stature VII Percentile and Quartile VIII Definitions IX Quartiles X Percentiles XI Excel Functions XII The Normal Distribution XIII Example XIV Example XV Normal Distributions XVI Definition XVII Definition XVIII Important Principles XIX Example Current Lecture I Definition a Z score or standardized value i The number of standard deviations that a given value x is above or below the mean ii Could be a statistic iii A z score of 0 is exactly average II Z scores a b c d Commonly used standard score Allows comparison and interpretation of virtually any distribution Can be calculated from interval and ratio scores only Indicates how many standard deviations a score is above or below the mean score e Communicates a score s relative location in a distribution III Interpreting Z Scores a Whenever a value is less than the mean its corresponding z score is negative i Ordinary values z score between 2 and 2 ii Unusual values z score 2 or z score 2 IV Normal Distribution a The famous bell curve b A very well defined distribution that is common in nature c 95 of the data in a normal distribution are in the interval 1 96 z 1 96 d e x axis is the unit of measurement f y axis is the frequency V Z Score Formulas a Sample i b Population i c Round z to 2 decimal places VI Example Male Stature a Male stature is normally distributed with a mean 5 9 and s d 3 b Michael Jordan is 6 6 What is his z score 6 6 78 and 5 9 69 i z 78 69 3 ii z 3 0 iii This is an unusually high z score VII Percentile and Quartile a Partition a set of sorted data according to relative number of values b min P1 P2 P3 P98 P99 max i There are only 99 percentiles ii 99 cuts iii On the GRE If you did better than 90 of people you re in the 90 th percentile c min Q1 Q2 Q3 max i Quartiles only split into 4 d Percentiles and Quartiles are used for summarizing sets of data e They are basically more types of descriptive statistics to describe data VIII Definitions a Q1 First Quartile separates the bottom 25 of sorted values from the top 75 i Always below median b Q2 Second Quartile same as the median separates the bottom 50 of sorted values from the top 50 c Q3 Third Quartile separates the bottom 75 of sorted values from the top 25 i Always above median IX Quartiles a Q1 Q2 Q3 b Divide ranked scores into four equal parts c d This is the 5 point summary X Percentiles a Just as there are three quartiles separating data into four parts there are 99 percentiles denoted P1 P2 P99 which partition the data into 100 groups XI Excel Functions a Percentile i PERCENTILE array k ii Returns the value of the kth percentile iii You do not have to sort the data XII XIII iv k would be from 0 1 v 80th percentile 80 vi 11th percentile 11 b Percentile Rank i PERCENTILERANK Array x ii Returns the rank of x as a percent of the data iii What percentage did I do better than iv X is the grade of 71 2 for example v It ll give you a number between 0 1 vi 39 means you only did better than 39 of the class The Normal Distribution a Table B1 describes the normal distribution in detail b Its in the back of the book c Example a Susan has a resting heart rate of 52 bpm which has a z score of 0 85 To which percentile is this closest we assume that it is normally distributed b c We use the table to look up the are under the curve XIV Example a Assume BMI is normally distributed with mean 27 1 kg m2 and s d 4 5 kg m2 b What percentage of the population has a BMI greater than 35 c z 36 27 4 5 d z 1 75556 e 3 92 XV Normal Distributions a Read chapter 8 in your textbook b Do questions 5 8 XVI Definition a Exploratory Data Analysis EDA the process of using statistical tools Such as graphs measures of center and measures of variation to investigate data sets in order to understand their important characteristics b This is what we do when we look over data for the first time and look for interesting things like outliers specific shaping etc XVII Definition a An outlier is a value that is located very far away from almost all of the other values XVIII Important Principles a An outlier can have a dramatic effect on the mean b An outlier can have a dramatic effect on the standard deviation c An outlier can have a dramatic effect on the scale of the histogram so that the true nature of the distribution is obscured XIX Example a Butterfly ballots in Palm Beach Country i 2000 U S Presidential Election ii There was an outlier here for sure