2009 Pearson Prentice Hall, Salkind. Chapter 7 Data Collection and Descriptive Statistics.

2009 Pearson Prentice Hall, Salkind.

Chapter 7Data 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


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


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


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


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 = X n

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

1. Add up all of the scores2. 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 scores3. Select middle score

How to compute it when n is even

1. Order scores from lowest to highest

2. Count number of scores3. 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 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



1. List scores and compute mean

X

13

14

15

12

13

14

13

16

15

9

X = 13.4




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




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




3. Square each deviation

4. Sum squared deviations





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


UNDERSTANDING DISTRIBUTIONS


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

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?

2009 Pearson Prentice Hall, Salkind. Chapter 7 Data Collection and Descriptive Statistics.

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