CHAPTER OVERVIEW

• Getting Ready for Data Collection• The Data Collection Process• Getting Ready for Data Analysis• Understanding Distributions

GETTING READY FOR DATA COLLECTION

Four steps

• Constructing a data collection form• Establishing a coding strategy• Collecting the data• Entering data onto the collection

form

GRADE

2.00 4.00 6.00 10.00 Total

gender

male 20 16 23 19 95

female

19 21 18 16 105

Total 39 37 41 35 200

THE DATA COLLECTION PROCESS

• Begins with raw data– Raw data are unorganized data

CONSTRUCTING DATA COLLECTION FORMS

ID Gender

Grade Building Reading Score

Mathematics Score

12345

22122

8284

10

16666

5541465645

6044375932

One column for each variable

One row for each subject

ADVANTAGES OF OPTICAL SCORING SHEETS

• If subjects choose from several responses, optical scoring sheets might be used – Advantages

• Scoring is fast• Scoring is accurate• Additional analyses are easily done

– Disadvantages• Expense

CODING DATA

• Use single digits when possible• Use codes that are simple and unambiguous• Use codes that are explicit and discrete 

 

Variable Range of Data Possible

Example

ID Number 001 through 200 138

Gender 1 or 2 2

Grade 1, 2, 4, 6, 8, or 10 4

Building 1 through 6 1

Reading Score 1 through 100 78

Mathematics Score 1 through 100 69

TEN COMMANDMENTS OF DATA COLLECTION1. Think about what data are needed to answer the

question2. Think about where the data will come from3. Be sure the data collection form is clear and easy to

use4. Make a duplicate of the original data5. Ensure that your assistants are well trained6. Schedule your data collection efforts7. Cultivate sources for finding participants8. Follow up on participants that you originally missed9. Don’t throw away original data10. Follow these guidelines

GETTING READY FOR DATA ANALYSIS

• Descriptive statistics—Basic measures– Average scores on a variable– How different scores are from one another

• Inferential statistics—Help make decisions about– Null and research hypotheses– Generalizing from sample to population

DESCRIPTIVE STATISTICS

• Distributions of Scores

• Comparing Distributions of Scores

MEASURES OF CENTRAL TENDENCY

• Mean—”average”• Median—midpoint in a distribution• Mode—most frequent score

• How to compute it– = X n

= summation sign• X = each score• n = size of sample

1. Add up all of the scores

2. Divide the total by the number of scores

X

MEAN

• What it is– Arithmetic

average– Sum of

scores/number of scores

• How to compute it when n is odd1. Order scores from

lowest to highest2. Count number of scores3. Select middle score

• How to compute it when n is even1. Order scores from

lowest to highest2. Count number of scores3. Compute X of two

middle scores

MEDIAN

• What it is– Midpoint of

distribution– Half of scores

above & half of scores below

MODE

• What it is– Most frequently

occurring score

• What it is not!– How often the

most frequent score occurs

WHEN TO USE WHICH MEASURE

Measure of Central

Tendency

Level of Measurement

Use When Examples

Mode Nominal Data are categorical Eye color, party affiliation

Median Ordinal Data include extreme scores

Rank in class, birth order

Mean Interval and ratio

You can, and the data fit

Speed of response, age in years

MEASURES OF VARIABILITY

Variability is the degree of spread or dispersion in a set of scores

• Range—difference between highest and lowest score

• Standard deviation—average difference of each score from mean

COMPUTING THE STANDARD DEVIATION

• s

= summation sign– X = each score– X = mean – n = size of sample

= (X – X)2

n - 1

COMPUTING THE STANDARD DEVIATION

• List scores and compute mean

X

13

14

15

12

13

14

13

16

15

9

X = 13.4

COMPUTING THE STANDARD DEVIATION

• List scores and compute mean

• Subtract mean from each score

X (X-X)

13 -0.4

14 0.6

15 1.6

12 -1.4

13 -0.4

14 0.6

13 -0.4

16 2.6

15 1.6

9 -4.4

X = 0X = 13.4

X

13 -0.4 0.16

14 0.6 0.36

15 1.6 2.56

12 -1.4 1.96

13 -0.4 0.16

14 0.6 0.36

13 -0.4 0.16

16 2.6 6.76

15 1.6 2.56

9 -4.4 19.36

X =13.4

X = 0  

COMPUTING THE STANDARD DEVIATION

• List scores and compute mean

• Subtract mean from each score

• Square each deviation

(X – X)2(X – X)

COMPUTING THE STANDARD DEVIATION

• List scores and compute mean

• Subtract mean from each score

• Square each deviation

• Sum squared deviations

X

13 -0.4 0.16

14 0.6 0.36

15 1.6 2.56

12 -1.4 1.96

13 -0.4 0.16

14 0.6 0.36

13 -0.4 0.16

16 2.6 6.76

15 1.6 2.56

9 -4.4 19.36

X =13.4

X = 0 X2 = 34.4

(X – X) (X – X)2

COMPUTING THE STANDARD DEVIATION

1. List scores and compute mean

2. Subtract mean from each score

3. Square each deviation4. Sum squared

deviations5. Divide sum of squared

deviation by n – 1• 34.4/9 = 3.82 (= s2)

6. Compute square root of step 5 3.82 = 1.95

X

13 -0.4 0.16

14 0.6 0.36

15 1.6 2.56

12 -1.4 1.96

13 -0.4 0.16

14 0.6 0.36

13 -0.4 0.16

16 2.6 6.76

15 1.6 2.56

9 -4.4 19.36

X =13.4

X = 0 X2 = 34.4

(X – X) (X – X)2

THE NORMAL (BELL SHAPED) CURVE

• Mean = median = mode• Symmetrical about midpoint• Tails approach X axis, but do not touch

THE MEAN AND THE STANDARD DEVIATION

STANDARD DEVIATIONS AND % OF CASES

• The normal curve is symmetrical• One standard deviation to either side of the mean contains 34% of

area under curve• 68% of scores lie within ± 1 standard deviation of mean

STANDARD SCORES: COMPUTING z SCORES

• Standard scores have been “standardized”

SO THAT• Scores from different distributions have

– The same reference point– The same standard deviation

• ComputationZ = (X – X)

s–Z = standard score

–X = individual score

–X = mean

–s = standard deviation

STANDARD SCORES: USING z SCORES

• Standard scores are used to compare scores from different distributions

Class Mean

Class Standard Deviation

Student’s Raw

Score

Student’s z Score

SaraMicah

9090

24

9292

1.5

WHAT z SCORES REALLY, REALLY MEAN• Because

– Different z scores represent different locations on the x-axis, and

– Location on the x-axis is associated with a particular percentage of the distribution

• z scores can be used to predict– The percentage of scores both above and

below a particular score, and– The probability that a particular score will

occur in a distribution