ie(ds)1 descriptive statistics data - quantitative observation of behavior what do numbers mean? if...

21
IE(DS) 1 riptive Statistics - Quantitative observation of Behavior do numbers mean? e call one thing 1 and her thing 2 what do ean?

Upload: alaina-dawson

Post on 18-Jan-2016

213 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: 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

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?

Page 2: 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

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

Page 3: 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

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

Page 4: 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

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.

Page 5: 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

IE(DS) 5

4. Ratio Scales – have all arithmetic properties.

It is important to keep the limitations of theScale in mind when making conclusions.

Page 6: 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

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

Page 7: 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

IE(DS) 7

Each number on the abscissa represents a range of which the reported number is the mid-point.

Frequency Polygon

0

2

4

6

8

1 2 3 4 5 6 7 8 9 10

Variable Measured

Fre

qu

en

cy

E.g., 5 represents scores from 4.5 to 5.49.

Page 8: 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

IE(DS) 8

Symmetrical Distribution

0

2

4

6

8

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

0

1

2

3

4

5

6

1 2 3 4 5 6 7 8 9 10

Variable Measured

Fre

qu

en

cy

Skewed Distributions - scores pile up on one end of the curve.Skewed Negitively

0

1

2

3

4

5

6

1 2 3 4 5 6 7 8 9 10

Variable Measured

Freq

uenc

y

Page 9: 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

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.

Page 10: 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

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 =

Page 11: 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

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.

Page 12: 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

IE(DS) 12

3. Mean - Arithmetic Average.

X = (X)/N = Sum of all the scores number of scores.

Requires an Interval or Ratio scale.

Page 13: 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

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.

Page 16: 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

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.

Page 17: 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

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).

Page 18: 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

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.

Page 19: 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

IE(DS) 19

Problem: Most people do not think in Squares.

i.e., 16 is only twice as dispersed as 4.

Page 20: 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

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.

Page 21: 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

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