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2009 Pearson Prentice Hall, Salkind.
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.
2009 Pearson Prentice Hall, Salkind.
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
2009 Pearson Prentice Hall, Salkind.
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
2009 Pearson Prentice Hall, Salkind.
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
2009 Pearson Prentice Hall, Salkind.
THE DATA COLLECTION PROCESS Begins with raw data
Raw data are unorganized data
2009 Pearson Prentice Hall, Salkind.
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
2009 Pearson Prentice Hall, Salkind.
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
2009 Pearson Prentice Hall, Salkind.
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
2009 Pearson Prentice Hall, Salkind.
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
2009 Pearson Prentice Hall, Salkind.
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
2009 Pearson Prentice Hall, Salkind.
DESCRIPTIVE STATISTICS Distributions of Scores
• Comparing Distributions of Scores
2009 Pearson Prentice Hall, Salkind.
MEASURES OF CENTRAL TENDENCY Mean—arithmetic average Median—midpoint in a distribution Mode—most frequent score
2009 Pearson Prentice Hall, Salkind.
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
2009 Pearson Prentice Hall, Salkind.
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
2009 Pearson Prentice Hall, Salkind.
MODE
What it is Most frequently occurring
score
What it is not! How often the most
frequent score occurs
2009 Pearson Prentice Hall, Salkind.
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
2009 Pearson Prentice Hall, Salkind.
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
2009 Pearson Prentice Hall, Salkind.
COMPUTING THE STANDARD DEVIATION
s
= summation sign X = each score X = mean n = size of sample
= (X – X)2
n - 1
2009 Pearson Prentice Hall, Salkind.
COMPUTING THE STANDARD DEVIATION
1. List scores and compute mean
X
13
14
15
12
13
14
13
16
15
9
X = 13.4
2009 Pearson Prentice Hall, Salkind.
COMPUTING THE STANDARD DEVIATION
1. List scores and 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
2009 Pearson Prentice Hall, Salkind.
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
1. List scores and compute mean
2. Subtract mean from each score
3. Square each deviation
(X – X)2(X – X)
2009 Pearson Prentice Hall, Salkind.
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 deviation
4. Sum squared deviations
2009 Pearson Prentice Hall, Salkind.
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
2009 Pearson Prentice Hall, Salkind.
THE NORMAL (BELL SHAPED) CURVE
Mean = median = mode Symmetrical about midpoint Tails approach X axis, but do not touch
2009 Pearson Prentice Hall, Salkind.
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
2009 Pearson Prentice Hall, Salkind.
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
2009 Pearson Prentice Hall, Salkind.
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
2009 Pearson Prentice Hall, Salkind.
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
2009 Pearson Prentice Hall, Salkind.
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?