Explain the steps in the data collection Data process. Construct a data collection form and code Collection and data collected. Descriptive Identify 10 “commandments” of data collection. Statistics 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. 2011 Pearson Prentice Hall, Salkind.
Compute the range, standard Getting Ready for Data Collection deviation, and variance from a set of scores. The Data Collection Process Explain measures of variability and Getting Ready for Data Analysis when each one should be used. Descriptive Statistics Discuss why the normal curve is important to the research process. ◦ Measures of Central Tendency ◦ Measures of Variability Compute a z-score from a set of scores. Understanding Distributions Explain what a z-score means.
2011 Pearson Prentice Hall, Salkind. 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. 2011 Pearson Prentice Hall, Salkind.
1 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. 2011 Pearson Prentice Hall, Salkind.
One column for each variable Begins with raw data ◦ Raw data are unorganized data ID Gender Grade Building Reading Mathematics Score Score 1 2 8 1 55 60 2 2 2 6 41 44 3 1 8 6 46 37 4 2 4 6 56 59 5 2 10 6 45 32
One row for each subject
2011 Pearson Prentice Hall, Salkind. 2011 Pearson Prentice Hall, Salkind.
Variable Range of Data Possible Example If subjects choose from several ID Number 001 through 200 138 responses, optical scoring sheets Gender 1 or 2 2 might be used Grade 1, 2, 4, 6, 8, or 10 4 ◦ Advantages Building 1 through 6 1 Scoring is fast Reading Score 1 through 100 78 Scoring is accurate Mathematics Score 1 through 100 69 Additional analyses are easily done Use single digits when possible ◦ Disadvantages Use codes that are simple and Expense unambiguous Use codes that are explicit and discrete
2011 Pearson Prentice Hall, Salkind. 2011 Pearson Prentice Hall, Salkind.
2 1. Get permission from your institutional review board to collect the data Descriptive statistics—basic measures 2. Think about the type of data you will have to collect ◦ Average scores on a variable 3. Think about where the data will come from ◦ How different scores are from one another 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 Inferential statistics—help make separate location decisions about 6. Ensure that those collecting data are well-trained ◦ Null and research hypotheses 7. Schedule your data collection efforts ◦ Generalizing from sample to population 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. 2011 Pearson Prentice Hall, Salkind.
Distributions of Scores
• Comparing Distributions of Scores
2011 Pearson Prentice Hall, Salkind. 2011 Pearson Prentice Hall, Salkind.
What it is How to compute it Mean—arithmetic average ◦ Arithmetic average ◦ X = ΣX n Median—midpoint in a distribution ◦ Sum of scores/number of Σ = summation sign Mode—most frequent score scores X = each score n = size of sample 1. Add up all of the scores 2. Divide the total by the number of scores
2011 Pearson Prentice Hall, Salkind. 2011 Pearson Prentice Hall, Salkind.
3 What it is How to compute it What it is What it is not! when n is odd ◦ Midpoint of 1. Order scores from ◦ Most frequently ◦ How often the most distribution lowest to highest occurring score frequent score ◦ Half of scores 2. Count number of occurs scores above and half of 3. Select middle score scores below How to compute it when n is even 1. Order scores from lowest to highest 2. Count number of scores 3. Compute X of two middle scores
2011 Pearson Prentice Hall, Salkind. 2011 Pearson Prentice Hall, Salkind.
Measure of Level of Use When Examples Variability is the degree of spread or Central Measurement dispersion in a set of scores Tendency
Mode Nominal Data are Eye color, RangeRange—difference between highest and categorical party lowest score affiliation Median Ordinal Data include Rank in class, Standard deviationdeviation—average difference of extreme birth order, each score from mean scores income Mean Interval and You can, and Speed of ratio the data fit response, age in years
2011 Pearson Prentice Hall, Salkind. 2011 Pearson Prentice Hall, Salkind.
X 1. List scores and 13 compute mean s 14 = ∑(X – X) 2 15 n - 1 ◦ Σ = summation sign 12 ◦ X = each score 13 ◦ X = mean 14 ◦ n = size of sample 13 16
15
9
X = 13.4
2011 Pearson Prentice Hall, Salkind. 2011 Pearson Prentice Hall, Salkind.
4 X (X-X) (X – X) 2 1. List scores and X (X – X) 1. List scores and 13 -0.4 compute mean 13 -0.4 0.16 compute mean 14 0.6 14 0.6 0.36 2. Subtract mean 15 1.6 2. Subtract mean 15 1.6 2.56 from each score 12 -1.4 from each 12 -1.4 1.96 3. Square each 13 -0.4 score 13 -0.4 0.16
14 0.6 14 0.6 0.36 deviation
13 -0.4 13 -0.4 0.16
16 2.6 16 2.6 6.76
15 1.6 15 1.6 2.56
9 -4.4 9 -4.4 19.36
X = 13.4 ∑X = 0 X =13.4 ∑ X = 0
2011 Pearson Prentice Hall, Salkind. 2011 Pearson Prentice Hall, Salkind.
2 X (X – X) (X – X) X 2 1. List scores and (X – X) (X – X) 1. List scores and 13 -0.4 0.16 compute mean 13 -0.4 0.16 compute mean 14 0.6 0.36 14 0.6 0.36 2. Subtract mean from 15 1.6 2.56 2. Subtract mean 15 1.6 2.56 each score 12 -1.4 1.96 3. Square each deviation from each score 12 -1.4 1.96 4. 13 -0.4 0.16 Sum squared deviations 3. Square each 13 -0.4 0.16 5. Divide sum of squared 14 0.6 0.36 deviation 14 0.6 0.36 deviation by n – 1 13 -0.4 0.16 2 4. Sum squared 13 -0.4 0.16 • 34.4/9 = 3.82 (= s ) 16 2.6 6.76 deviations 16 2.6 6.76 6. Compute square root 15 1.6 2.56 15 1.6 2.56 of step 5 √ 9 -4.4 19.36 9 -4.4 19.36 • 3.82 = 1.95
∑ ∑ 2 X =13.4 X = 0 X = X =13.4 ∑ X = 0 ∑ X2 = 34.4 34.4
2011 Pearson Prentice Hall, Salkind. 2011 Pearson Prentice Hall, Salkind.
Mean = median = mode Symmetrical about midpoint Tails approach X axis, but do not touch
2011 Pearson Prentice Hall, Salkind. 2011 Pearson Prentice Hall, Salkind.
5 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. 2011 Pearson Prentice Hall, Salkind.
Standard scores have been “standardized” Standard scores are used to compare scores SO THAT Scores from different distributions have from different distributions ◦ the same reference point ◦ the same standard deviation Class Class Student’s Student’s Computation Mean Standard Raw z Score Z = (X – X) Deviation Score s Sara 90 2 92 1 –Z = standard score Micah 90 4 92 .5 –X = individual score –X = mean –s = standard deviation
2011 Pearson Prentice Hall, Salkind. 2011 Pearson Prentice Hall, Salkind.
Because Explain the steps in the data collection process? ◦ Different z scores represent different Construct a data collection form and code data collected? locations on the x-axis, and Identify 10 “commandments” of data collection? ◦ Location on the x-axis is associated Define the difference between inferential and descriptive statistics? with a particular percentage of the Compute the different measures of central tendency from a set of distribution scores? Explain measures of central tendency and when each one should be z scores can be used to predict used? ◦ The percentage of scores both above Compute the range, standard deviation, and variance from a set of and below a particular score, and scores? ◦ The probability that a particular score Explain measures of variability and when each one should be used? will occur in a distribution 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. 2011 Pearson Prentice Hall, Salkind.
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