2011 pearson prentice hall, salkind. chapter 7 data collection and descriptive statistics

2011 Pearson Prentice Hall, Salkind.

Data Collection and Descriptive Statistics


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.


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


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


Begins with raw data◦ Raw data are unorganized data


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


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


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


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


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


Distributions of Scores

• Comparing Distributions of Scores


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

What it is◦ Arithmetic

average◦ Sum of

scores/number of scores

X


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 even1. Order scores from

lowest to highest2. Count number of

scores3. Compute X of two

middle scores

What it is◦ Midpoint of

distribution◦ Half of scores

above and half of scores below


What it is◦ Most frequently

occurring score

What it is not!◦ How often the

most frequent score occurs


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, income

Mean Interval and ratio

You can, and the data fit

Speed of response, age in years


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


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


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


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 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 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


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


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?

2011 pearson prentice hall, salkind. chapter 7 data collection and descriptive statistics

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