Review of Descriptive Statistics Student PDF

Review of Descriptive Please don’t forget to sign the attendance Statistics sheet and grab a set of colored notecards.  Descriptive Statistics: Why Summarize Data? "Descriptive Statistics": Procedures used to summarize, organize, and make sense of a set of...

Review of Descriptive Please don’t forget to sign the attendance Statistics sheet and grab a set of colored notecards.  Descriptive Statistics: Why Summarize Data? "Descriptive Statistics": Procedures used to summarize, organize, and make sense of a set of scores or observations, typically presented graphically, in a table, or as summary statistics (single values) Two main reasons why we summarize data using descriptive statistics: o To clarify what patterns were observed in a data set at a glance. o To be concise.  Measures of Central Tendency "Central Tendency": Statistical measures for locating a single score that tends to be near the center of a distribution and is most representative or descriptive of all scores in a distribution. Three measures: o "Mean": The sum of all scores divided by the number of scores summed in a sample o "Median": The middle value in a distribution of data listed in numeric order o "Mode": The value in a data set that occurs the most often or most frequently "Normal Distribution": A theoretical distribution with data that are symmetrically distributed around the mean, median, and the mode  Z-Score Distribution “Z Scores”: Standard scores that describe the differences in individual values from the mean in units of standard deviation. Positive Z scores are above the mean and negative Z scores are below the mean. The magnitude of the Z score describes the distance between the value and the mean in number of standard deviation units. The shape of the distribution does not change.  Z-Score Distribution “The Empirical Rule”: States that about 68% of the values fall within 1 standard deviation from the mean, about 95% the values fall within 2 standard deviations from the mean, and about 99.7% of the values fall within 3 standard deviations from the mean. Also called the “68-95-99.7” rule.  Outliers “Outliers”: Extreme values in a distribution. Usually far away from the rest of the data points Beware of outliers. They have the potential to heavily influence the results. In terms of the measure of central tendency, which one do you think is most influenced by outliers? The mean  Measures of Variability "Variability": A measure of the dispersion or spread of scores in a distribution. Three measures of variability: o "Range": The difference between the largest value and the smallest value in a data set. o "[Sample] Variance": A measure of variability for the average squared distance that scores in a sample deviate from the sample mean. o "Standard Deviation": A measure of variability for the average distance that scores in a sample deviate from the sample mean and is computed by taking the square root of the sample variance. ▪ In a normal distribution, most scores fall within one standard deviation of the mean, and almost all scores fall within three standard deviations of the mean. Types of Variables "Continuous Variable": measured along a continuum at any place beyond the decimal point, meaning that it can be measured in whole units or fractional units Race times "Discrete Variable": measured in whole units or categories that are not distributed along a continuum Number of people in this class Scales of Measurement "Scales of Measurement": Rules for how the properties of numbers can change with different uses. Developed by S. S. Stevens in early 1940s Nominal, Ordinal, Interval, Ratio All based on three questions Order: Does a larger number indicate a greater value than a smaller number? Differences: Does subtracting one set of numbers represent some meaningful value? Ratio: Does dividing, or taking the ratio of, one set of numbers represent some meaningful value? Nominal "Nominal Scales": Measurements in which a number is assigned to represent something or someone. Often referred to as coded values Zip codes; license plate numbers; telephone numbers No one is greater than another Ordinal "Ordinal Scale": Measurements than convey order or rank only Finishing order in a competition; education level; ranking Differences between ranks do not have meaning Interval "Interval Scales": Measurements that have no true zero and are distributed in equal units The rating scale (rate how satisfied you are from 1-7) Temperature Ratio "Ratio Scales": Measurements that have a true zero and are equidistant "True Zero": When the value of 0 truly indicates nothing on a scale of measurement. Height; weight; time Different Scales of Measurement and the Information They Provide Concerning the Order, Difference, and Ratio of Numbers Scale of Measurement Nominal Ordinal Interval Ratio Order NO YES YES YES Property Difference NO NO YES YES Ratio NO NO NO YES Any Questions?