2011 pearson prentice hall, salkind. chapter 7 data collection and descriptive statistics
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2011 Pearson Prentice Hall, Salkind.
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.
2011 Pearson Prentice Hall, Salkind.
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.
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
2011 Pearson Prentice Hall, Salkind.
Constructing a data collection form Establishing a coding strategy Collecting the data Entering data onto the collection
form
2011 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
2011 Pearson Prentice Hall, Salkind.
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
2011 Pearson Prentice Hall, Salkind.
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
2011 Pearson Prentice Hall, Salkind.
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
2011 Pearson Prentice Hall, Salkind.
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
2011 Pearson Prentice Hall, Salkind.
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
2011 Pearson Prentice Hall, Salkind.
Mean—arithmetic average Median—midpoint in a distribution Mode—most frequent score
2011 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
What it is◦ Arithmetic
average◦ Sum of
scores/number of scores
X
2011 Pearson Prentice Hall, Salkind.
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
2011 Pearson Prentice Hall, Salkind.
What it is◦ Most frequently
occurring score
What it is not!◦ How often the
most frequent score occurs
2011 Pearson Prentice Hall, Salkind.
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
2011 Pearson Prentice Hall, Salkind.
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
2011 Pearson Prentice Hall, Salkind.
s
◦ = summation sign◦ X = each score◦ X = mean ◦ n = size of sample
= (X – X)2
n - 1
2011 Pearson Prentice Hall, Salkind.
1. List scores and compute mean
X
13
14
15
12
13
14
13
16
15
9
X = 13.4
2011 Pearson Prentice Hall, Salkind.
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
2011 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
1. List scores and compute mean
2. Subtract mean from each score
3. Square each deviation
(X – X)2(X – X)
2011 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
1. List scores and compute mean
2. Subtract mean from each score
3. Square each deviation
4. Sum squared deviations
2011 Pearson Prentice Hall, Salkind.
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
2011 Pearson Prentice Hall, Salkind.
Mean = median = mode Symmetrical about midpoint Tails approach X axis, but do not touch
2011 Pearson Prentice Hall, Salkind.
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
2011 Pearson Prentice Hall, Salkind.
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
2011 Pearson Prentice Hall, Salkind.
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
2011 Pearson Prentice Hall, Salkind.
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
2011 Pearson Prentice Hall, Salkind.
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?