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Chapter 7

- Data 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

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

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

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

TEN COMMANDMENTS OF DATA COLLECTION

- Get permission from your institutional review

board to collect the data - Think about the type of data you will have to

collect - Think about where the data will come from
- Be sure the data collection form is clear and

easy to use - Make a duplicate of the original data and keep it

in a separate location - Ensure that those collecting data are

well-trained - Schedule your data collection efforts
- Cultivate sources for finding participants
- Follow up on participants that you originally

missed - Dont throw away original data

GETTING READY FOR DATA ANALYSIS

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

DESCRIPTIVE STATISTICS

DESCRIPTIVE STATISTICS

- Distributions of Scores

- Comparing Distributions of Scores

MEASURES OF CENTRAL TENDENCY

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

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

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

MODE

- What it is
- Most frequently occurring score

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

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

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

COMPUTING THE STANDARD DEVIATION

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

COMPUTING THE STANDARD DEVIATION

- List scores and compute mean

COMPUTING THE STANDARD DEVIATION

- List scores and compute mean
- Subtract mean from each score

COMPUTING THE STANDARD DEVIATION

- List scores and compute mean
- Subtract mean from each score
- Square each deviation

COMPUTING THE STANDARD DEVIATION

- List scores and compute mean
- Subtract mean from each score
- Square each deviation
- Sum squared deviations

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

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
- Computation

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

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?