3 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 0 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. Chapter Objectives, Continued Students Should Be Able To: 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. 4 5 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 6 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 7 8 THE DATA COLLECTION PROCESS 9 THE DATA COLLECTION PROCESS Begins with raw data Raw data are unorganized data
0 CONSTRUCTING DATA COLLECTION FORMS 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 Use single digits when possible Use codes that are simple and unambiguous Use codes that are explicit and discrete 3 4 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 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 0. Don t throw away original data 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 5 6 7 DESCRIPTIVE STATISTICS DESCRIPTIVE STATISTICS Distributions of Scores MEASURES OF CENTRAL TENDENCY Mean arithmetic average Median midpoint in a distribution
8 Mode most frequent score MEAN How to compute it = ΣX n Σ = 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 9 MEDIAN How to compute it when n is odd. Order scores from lowest to highest. Count number of scores 3. Select middle score How to compute it when n is even. Order scores from lowest to highest. Count number of scores 3. Compute X of two middle scores What it is Midpoint of distribution Half of scores above and half of scores below 0 MODE What it is Most frequently occurring score What it is not! How often the most frequent score occurs WHEN TO USE WHICH MEASURE 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 3 s 3
Σ = summation sign X = each score X = mean n = size of sample 4 5 6 7 8 9 30 3 3 33. Subtract mean from each score. Subtract mean from each score. Subtract mean from each score 4. Sum squared deviations. Subtract mean from each score 4. Sum squared deviations 5. Divide sum of squared deviation by n 34.4/9 = 3.8 (= s ) 6. Compute square root of step 5 3.8 =.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 ± standard deviation of mean STANDARD SCORES: COMPUTING z SCORES Standard scores have been standardized 4
SO THAT Scores from different distributions have the same reference point the same standard deviation Computation 34 35 36 STANDARD SCORES: USING z SCORES Standard scores are used to compare scores from different distributions 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 0 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? 5