IE(DS)1 Descriptive Statistics Data - Quantitative observation of Behavior What do numbers mean? If we call one thing 1 and another thing 2 what do we mean?

IE(DS)2 Properties of Measurement Scales 1. Difference – Nominal labels 2. Order – Ranking of value 3. Equal Intervals – Each numeric step is of equal value. *Addition & subtraction 4.Ratio – natural falling zero (zero means “none” of the quality being measured. *multiplication and division

IE(DS)3 Categorical Scales Nominal Scales – Just name categories. - no order or arithmetic properties implied. e.g., Sex 1 = male; 2 = female Ordinal Scales – rank ordering but not equal Intervals  no arithmetic properties. e.g., Private, Lieutenant, Major, General

IE(DS)4 Continuous Scales 3. Interval Scale – Difference,Order and Equal Intervals. e.g., Temp Is 64  twice as warm as 32  ? Does 0  mean there is no temperature? Has addition and subtraction properties, (64 is as much warmer than 62 as 65 is warmer than 63) But not multiplication or division.

IE(DS)5 4.Ratio Scales – have all arithmetic properties. It is important to keep the limitations of the Scale in mind when making conclusions.

IE(DS)6 Frequency Distributions: Histogram Ordinate (y-axis): Frequency Abscissa (X-axis): Dependant Variable

IE(DS)7 Each number on the abscissa represents a range of which the reported number is the mid-point. E.g., 5 represents scores from 4.5 to 5.49.

IE(DS)8 Distribution of Scores Symmetrical - scores evenly distributed around the mid-point of the distribution. Skewed Distributions - scores pile up on one end of the curve.

IE(DS)9 Measures of Central Tendency - Typical or Average Score 1. Mode - Most frequent score. - can have more than one Mode (e.g., bimodal or Trimodal). Fairly unstable - can be effected by one or two scores. 2,2,2,2,3,3,3,3,3,4,4,4,4,5,5 Mode = 3 2,2,2,2,2,3,3,3,3,4,4,4,4,5,5 Mode = 2 Can be used with any type of scale.

IE(DS)10 2. Median - Middle score, 50th Percentile Uneven number of scores - just the mid-point. E.g. 2,2,3,4,4,5,6,6,7 Median = When even number - add 2 middle scores and divide by 2 2, 2, 3,4, 4,5,6, 6, 7, 7 Median =

IE(DS)11 Medians can not be used with Nominal Data. Medians are fairly stable. Insensitive to extreme scores. E.g, 2,2,3,4,5,5,6,7,7 Median = 4 2,2,3,4,4,5,6,6,20 Median is still 4.

IE(DS)12 3. Mean - Arithmetic Average. X = (  X)/N = Sum of all the scores number of scores. Requires an Interval or Ratio scale.

IE(DS)13 In a symmetrical, unimodal, distribution the Mode, Median and Mean will all be the same. When the distribution is skewed, or contains some deviant scores, these three measures can be very different.

IE(DS)14 Source

IE(DS)15 Source

IE(DS)16 Measures of Dispersion Range - Difference between the highest and lowest category = 9 Strongly effected by extreme scores. Must be at least ordinal scale.

IE(DS)17 Deviation Scores (Interval or Ratio) Total of each score minus the mean. Problem: This will always be zero. Total above mean (+ scores) will always equal total below the mean (- scores).

IE(DS)18 Variance Uses a mathematicians trick! All squared numbers are positive. Variance = deviation scores squared Number of scores Sum now does not equal zero.

IE(DS)19 Problem: Most people do not think in Squares. i.e., 16 is only twice as dispersed as 4.

IE(DS)20 Standard Deviation (s) - square root of variance. 4 compared to 16 2 compared to 4 Average amount that scores deviate from the mean.

IE(DS)21 Most measures fall on a normal curve - most frequent score is mean - as scores get more extreme they are less frequent - symmetric distribution - asymptotic Standard Deviations