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IE(DS) 1
Descriptive Statistics
Data - Quantitative observation of Behavior
What do numbers mean?
If we call one thing 1 andanother thing 2 what dowe mean?
IE(DS) 2
Properties of Measurement Scales1. Difference – Nominal labels2. Order – Ranking of value3. 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 ScalesNominal 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 Scales3. Interval Scale – Difference,Order and Equal
Intervals. e.g., TempIs 64 twice as warm as 32? Does 0 mean there is no temperature?Has addition and subtraction properties, (64 is asmuch 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 theScale in mind when making conclusions.
IE(DS) 6
Frequency Distributions: Histogram
Frequency Histogram
0
2
4
6
8
1 2 3 4 5 6 7 8 9 10
Variable Measured
Fre
qu
en
cy
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.
Frequency Polygon
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1 2 3 4 5 6 7 8 9 10
Variable Measured
Fre
qu
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cy
E.g., 5 represents scores from 4.5 to 5.49.
IE(DS) 8
Symmetrical Distribution
0
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1 2 3 4 5 6 7 8 9 10
Variable Measured
Freq
uenc
y
Distribution of Scores
Symmetrical - scores evenly distributed around the mid-point of the distribution.
Skewed Positivily
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1 2 3 4 5 6 7 8 9 10
Variable Measured
Fre
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Skewed Distributions - scores pile up on one end of the curve.Skewed Negitively
0
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1 2 3 4 5 6 7 8 9 10
Variable Measured
Freq
uenc
y
IE(DS) 9
Measures of Central Tendency - Typical or Average Score1. 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 = 32,2,2,2,2,3,3,3,3,4,4,4,4,5,5 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 = 42,2,3,4,4,5,6,6,20 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) 15Source
IE(DS) 16
Measures of Dispersion
Range - Difference between the highest and lowest category. 10.5 - 1.5 = 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 alwaysequal total below the mean (- scores).
IE(DS) 18
VarianceUses 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
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