Data Collection and Descriptive Statistics

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Chapter 7

• Data Collection and Descriptive Statistics

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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.

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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

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GETTING READY FOR DATA COLLECTION
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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

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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
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THE DATA COLLECTION PROCESS
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THE DATA COLLECTION PROCESS

• Begins with raw data
• Raw data are unorganized data

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CONSTRUCTING DATA COLLECTION FORMS
One column for each variable
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 row for each subject
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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

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CODING DATA
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

• Use single digits when possible
• Use codes that are simple and unambiguous
• Use codes that are explicit and discrete

   
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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. Dont throw away original data

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GETTING READY FOR DATA ANALYSIS
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GETTING READY FOR DATA ANALYSIS

• Descriptive statisticsbasic measures
• Average scores on a variable
• How different scores are from one another
• Inferential statisticshelp make decisions about
• Null and research hypotheses
• Generalizing from sample to population

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DESCRIPTIVE STATISTICS
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DESCRIPTIVE STATISTICS

• Distributions of Scores

• Comparing Distributions of Scores

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MEASURES OF CENTRAL TENDENCY

• Meanarithmetic average
• Medianmidpoint in a distribution
• Modemost frequent score

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MEAN

• How to compute it
• ?X
• n
• ? summation sign
• X each score
• n size of sample
• Add up all of the scores
• Divide the total by the number of scores

• What it is
• Arithmetic average
• Sum of scores/number of scores

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MEDIAN

• How to compute it when n is odd
• Order scores from lowest to highest
• Count number of scores
• Select middle score
• How to compute it when n is even
• Order scores from lowest to highest
• Count number of scores
• Compute X of two middle scores

• What it is
• Midpoint of distribution
• Half of scores above and half of scores below

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MODE

• What it is
• Most frequently occurring score

• What it is not!
• How often the most frequent score occurs

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WHEN TO USE WHICH MEASURE
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
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MEASURES OF VARIABILITY

• Variability is the degree of spread or dispersion
  in a set of scores
• Rangedifference between highest and lowest score
• Standard deviationaverage difference of each
  score from mean

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COMPUTING THE STANDARD DEVIATION

• s
• ? summation sign
• X each score
• X mean
• n size of sample

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COMPUTING THE STANDARD DEVIATION

1. List scores and compute mean

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COMPUTING THE STANDARD DEVIATION

1. List scores and compute mean
2. Subtract mean from each score

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COMPUTING THE STANDARD DEVIATION

1. List scores and compute mean
2. Subtract mean from each score
3. Square each deviation

 
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COMPUTING THE STANDARD DEVIATION

1. List scores and compute mean
2. Subtract mean from each score
3. Square each deviation
4. Sum squared deviations

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COMPUTING THE STANDARD DEVIATION

• List scores and compute mean
• Subtract mean from each score
• Square each deviation
• Sum squared deviations
• Divide sum of squared deviation by n 1
• 34.4/9 3.82 ( s2)
• Compute square root of step 5
• ?3.82 1.95

 
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UNDERSTANDING DISTRIBUTIONS
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THE NORMAL (BELL SHAPED) CURVE

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

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THE MEAN AND THE STANDARD DEVIATION
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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

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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

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STANDARD SCORES USING z SCORES

• Standard scores are used to compare scores from
  different distributions

Class Mean Class Standard Deviation Students Raw Score Students z Score
Sara Micah 90 90 2 4 92 92 1 .5
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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

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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?