KIN 4310 1nd Edition Lecture 10Outline of Last Lecture I. Section 2 TopicsII. What is The Truth?III. ValidityIV. Validity: The IdeaV. ValidityVI. Content ValidityVII. Criterion ValidityVIII. Predictive & Concurrent ValidityIX. Construct ValidityX. ReliabilityXI. ValidityXII. ExampleXIII. Validity and ReliabilityXIV. Take-home MessagesXV. Reliability and ValidityOutline of Current Lecture I. DefinitionII. Z-ScoresThese 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 ScoresIV. Normal DistributionV. Z Score FormulasVI. Example: Male StatureVII. Percentile and QuartileVIII. DefinitionsIX. QuartilesX. PercentilesXI. Excel FunctionsXII. The Normal DistributionXIII. ExampleXIV. ExampleXV. Normal DistributionsXVI. DefinitionXVII. DefinitionXVIII. Important PrinciplesXIX. ExampleCurrent LectureI. Definitiona. Z-score (or standardized value)i. The number of standard deviations that a given value x is above or below the meanii. Could be a statisticiii. A z-score of 0 is exactly averageII. Z-scoresa. Commonly used standard scoreb. Allows comparison and interpretation of virtually any distribution c. Can be calculated from interval and ratio scores only!d. Indicates how many standard deviations a score is above or below the mean scoree. Communicates a score’s relative location in a distributionIII. Interpreting Z Scoresa. Whenever a value is less than the mean, its corresponding z score is negativei. Ordinary values: z score between -2 and 2ii. Unusual values: z score < -2 or z score > 2IV. Normal Distributiona. The famous bell curveb. A very well defined distribution that is common in naturec. 95% of the data in a normal distribution are in the interval -1.96 < z < 1.96d.e. x-axis is the unit of measurementf. y-axis is the frequencyV. Z Score Formulasa. Samplei.b. Populationi.c. Round z to 2 decimal placesVI. Example: Male Staturea. 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)/3ii. z = 3.0iii. This is an unusually high z scoreVII. Percentile and Quartilea. Partition a set of sorted data according to relative number of valuesb. min, P1, P2, P3, … P98, P99, maxi. There are only 99 percentilesii. “99 cuts”iii. On the GRE, If you did better than 90% of people, you’re in the 90th percentilec. min, Q1, Q2, Q3, maxi. Quartiles only split into 4d. Percentiles and Quartiles are used for summarizing sets of datae. They are basically more types of descriptive statistics to describe dataVIII. Definitionsa. Q1 (First Quartile) separates the bottom 25% of sorted values from the top 75%i. Always below medianb. 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 medianIX. Quartilesa. Q1, Q2, Q3b. Divide ranked scores into four equal partsc.d. This is the 5 point summaryX. Percentilesa. 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 groupsXI. Excel Functionsa. Percentilei. =PERCENTILE(array, k)ii. Returns the value of the kth percentileiii. You do not have to sort the dataiv. k would be from 0-1v. 80th percentile? .80vi. 11th percentile? .11b. Percentile Ranki. =PERCENTILERANK(Array, x)ii. Returns the rank of x as a percent of the dataiii. What percentage did I do better than __?iv. X is the grade of 71.2 for examplev. It’ll, give you a number between 0 -1vi. .39 means you only did better than 39% of the classXII. The Normal Distributiona. Table B1 describes the normal distribution in detailb. Its in the back of the bookc.XIII. Examplea. 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 curveXIV. Examplea. Assume BMI is normally distributed with mean = 27.1 kg/m2 and s.d. = 4.5 kg/m2b. What percentage of the population has a BMI greater than 35?c. z = (36-27)/4.5d. z = 1.75556e. 3.92%XV. Normal Distributionsa. Read chapter 8 in your textbookb. Do questions 5-8XVI. Definitiona. 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 characteristicsb. 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. Definitiona. An outlier is a value that is located very far away from almost all of the other valuesXVIII. Important Principlesa. An outlier can have a dramatic effect on the meanb. An outlier can have a dramatic effect on the standard deviationc. An outlier can have a dramatic effect on the scale of the histogram so that the true nature of the distribution is obscured.XIX. Examplea. Butterfly ballots in Palm Beach Countryi. 2000 U.S. Presidential Electionii. There was an outlier here for