salkind ppt ch07 - troy universitytrop.troy.edu/drsmall/class stuff/cp6691/salkind/mid-term...

2009 Pearson Prentice Hall, Salkind. 1

Chapter 7

Data Collection

and Descriptive

Statistics


CHAPTER OBJECTIVES -

STUDENTS SHOULD BE ABLE TO:� Explain the steps in the data collection process.� Construct a data collection form and code data collected.� Identify 10 “commandments” of data collection.� Define the difference between inferential and descriptive statistics.� Compute the different measures of central tendency from a set of

scores.� Explain measures of central tendency and when each one should be

used.� Compute the range, standard deviation, and variance from a set of

scores.� Explain measures of variability and when each one should be used.� Discuss why the normal curve is important to the research process.� Compute a z-score from a set of scores.� Explain what a z-score means.


CHAPTER OVERVIEW

� Getting Ready for Data Collection

� The Data Collection Process

� Getting Ready for Data Analysis

� Descriptive Statistics

� Measures of Central Tendency

� Measures of Variability

� 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

Total39 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

1

2

3

4

5

2

2

1

2

2

8

2

8

4

10

1

6

6

6

6

55

41

46

56

45

60

44

37

59

32

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 COLLECTION

1. Get permission from your institutional review board to collect the data

2. Think about the type of data you will have to collect

3. Think about where the data will come from

4. Be sure the data collection form is clear and easy to use

5. Make a duplicate of the original data and keep it in a separate location

6. Ensure that those collecting data are well-trained

7. Schedule your data collection efforts

8. Cultivate sources for finding participants

9. Follow up on participants that you originally missed

10. Don’t throw away original data


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—arithmetic average

� Median—midpoint in a distribution

� Mode—most frequent score


� How to compute it� = ΣX

n

� Σ = 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 odd

1. Order scores from lowest to highest

2. Count number of scores

3. Select middle score

� How to compute it when n is even

1. Order scores from lowest to highest

2. Count number of scores

3. Compute X of two middle scores

MEDIAN

� What it is

� Midpoint of distribution

� Half of scores above and 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

MEASUREMeasure 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, income

Mean Interval and ratio

You can, and the data fit

Speed of response, age in years


MEASURES OF VARIABILITYVariability 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

� Σ = summation sign

� X = each score

� X = mean

� n = size of sample

= ∑(X – X)2

n - 1

�


COMPUTING THE STANDARD

DEVIATION1. List scores and

compute mean

X

13

14

15

12

13

14

13

16

15

9

X = 13.4




compute mean

2. 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



compute mean

2. Subtract mean from

each score

3. Square each

deviation

(X – X)2(X – X)


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



compute mean


3. Square each deviation

4. Sum squared deviations



DEVIATION1. List scores and compute

mean


3. Square each deviation

4. Sum squared deviations

5. 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


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

� Computation Z = (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

Sara

Micah

90

90

2

4

92

92

1

.5


WHAT z SCORES 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


HAVE WE MET OUR

OBJECTIVES? CAN YOU:� Explain the steps in the data collection process?� Construct a data collection form and code data collected?� Identify 10 “commandments” of data collection?� Define the difference between inferential and descriptive statistics?� Compute the different measures of central tendency from a set of

scores?� Explain measures of central tendency and when each one should be

used?� Compute the range, standard deviation, and variance from a set of

scores?� Explain measures of variability and when each one should be used?� Discuss why the normal curve is important to the research process?� Compute a z-score from a set of scores?� Explain what a z-score means?

salkind ppt ch07 - troy universitytrop.troy.edu/drsmall/class stuff/cp6691/salkind/mid-term...

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