Introduction toQuantitative Analysis...Quantitative data canbeexpressed as a number or canbe...
Transcript of Introduction toQuantitative Analysis...Quantitative data canbeexpressed as a number or canbe...
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Introduction to Quantitative Analysis
MANSUREH KEBRITCHI, PH.D.
CENTER FOR EDUCATIONAL AND INSTRUCTIONALTECHNOLOGY RESEARCH(CEITR)
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Agenda
Quantitative AnalysisSteps
• Selecting statistical analysis
• Data entry
Definition of BasicConcepts
•Sample size
Basic analysis
•Descriptive and inferential
Resources
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What is Quantitative Data?
Quantitative data can be expressed as a number or can be quantified.
Quantitative data can be measured by numerical variables.
• Itcan be quantified, verified, and counted.
• Can be collected from tests, surveys, reports.
Examples
• Scores on tests andexams e.g. 85, 67, 90.
• The weight of a person or a subject.
• The number of hours ofstudy.
• The square feet of an apartment.
• The temperature in a room.
• The volume of a gas.
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Quantitative Analysis Selection
Criteria
Identify focus of your study, research questions, design
Identify your variables
Identify level of measurements of your variables
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Variables
A variable is defined as anything that has a quantity or quality that varies.
The dependent variable is the variable a researcher isinterested in.
An independent variable is a variable believed to affect the dependent variable.
Confounding variables are defined as interference caused by another variable
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Levels of Measurements
Nominal (categorical)
• Categories with no order, e.g., gender
Ordinal (categorical)
• Ordered categories,e.g., students’ grades
Interval (continuous)
• Ordered responses, equally spaced, no starting point e.g., temperature,
Ratio (Continuous)
• Variable has an absolute zero, e.g., length, weight
Note. In SPSS, interval & ratio data are considered “scale”, and
nominal and ordinal data have their own categories
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Quantitative Research DesignsDesigns Focus of the study Hypothesis Intervention Statisticalanalysis Example
Non-experimental
Survey
(nohypothesis)
Observational; Describe
the variables
No No Continuous V:Mean, STD,
Categorical
V: Mode
Description ofteenagers’
attitudes toward
smoking
Non-experimental
Correlation
Test relationships;
Prediction (criterion and
predictor variables)
Yes No Interval/ratio V:Pearson r
Regression
Ordinal V:
Spearman
Relationship
between IQand
clinical depression
Non-experimentalCausal-
comparative
(ex post facto)
Test cause and effectafter the effect occurred
(independent &
dependent variables)
Yes No Interval/ratio DV:T-test, Anova,
Nominal DV:
Chi Square
Effect offree/reduced
lunch on students’
performance
Quasi experimental Test cause and effect;Not a true random
sampling
(independent &
dependent variables)
Yes Yes Interval/ratio DV:T-test, Anova,
Nominal DV:
Chi Square
Effect of afterschool program on
childhood obesity
rate.
Experimental Test Cause and effect;Random sampling
(independent &
dependent variables)
Yes Yes Interval/ratio DV:T-test, Anova,
Nominal DV:
Chi Square
Effect of a newdiet treatmenton
insulin levels in
diabetics
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Quantitative Sample Size Depends on
Effect Size (ES): measures the strength of the relationship between two variables on a numeric scale; small, medium, large
Significance Criterion, α (P-Value): The riskof mistakenly rejectinga true null hypothesis (H); 0.05
• type Ierror is the rejection of a true null hypothesis
Power: the probability that it will reject a false null hypothesis; .80
• type IIerror is the non-rejection of a false null hypothesis
Analysis Test
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Quantitative Sample Size, Cohen (1991)
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Quantify and codingData
Before we can do any kind of analysis, we need to quantify ourdata
“Quantification” is the process of converting datato a numeric format
• Convert social science data into a “machine-readable” form, aform that can be read & manipulated by computer programs
Assign numeric representations tovariables:
• Turningmale into “1” and female into “2”
• Assigning “3” to Very Interested, “2” to Somewhat Interested,“1” to NotInterested
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Coding QuantitativeData
Goal – reduce a wide variety of information to a more limited set of variable attributes:
• Example, “What is youroccupation?”
• Use pre-established scheme: Professional, Managerial, Clerical, Semi-skilled,etc.
• Create a scheme after reviewing the data
• Assign value to each category in the scheme: Professional = 1, Managerial =2, etc.
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Select a software and
enter the data
Excel Spread Sheet,SPSS,
Create variables/column headings & enter each case
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Entering Data toSPSS
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Entering Data toSPSS
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SPSS videos https://ecampus.phoenix.edu/secure/aapd/cm e/spss/tutorial/index.asp
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Statistics Analysis Videos https://ecampus.phoenix.edu/secure/aapd/AO/SPSS/
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Basic Analysis
Descriptive statistics
• Describe what the data on hand show, such as:
• Distribution (frequency), Measures of central tendency (Mean, Mode), Measure of dispersion (Range, standard deviation)
Inferential statistics
• Allow you to make inferences about the population based on the data from your sample, such as:
• Paired-Samples t test
• Independent Samples ttest
• More complex: Correlation, Anova, Ancova, Regression
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Descriptive Statistics
1. Measures of Distribution
• Frequency distribution
• Listing every value Vs. grouping data into categories
• Counts Vs.percentages
2. Measures of Central Tendency
• Mean (average)
• Median (middle)
• Mode (mostcommon)
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Descriptive Statistics
3. Measure ofdispersion/spread of values
• Range: highest minus lowest• Standard deviation: distance from mean
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Inferential Statistics, Paired Samplet-test
Paired Sample t-test
• Samples are related
• Compare two samplemeans
• Same sample has been tested twice (pre/post)
Example
• In study on students’ math grades , allstudents are tested before receiving atreatment andafter the treatment
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Inferential Statistics, Independent Sample
t-test
Independent Sample t-test
• Two samples drawn independently of each other
• Test for difference in sample mean from two groups
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Inferential Statistics
Independent Sample t-test
Example
• Suppose the students are randomly assigned to a control and treatmentgroups
• Participants in the treatment group are given the treatment (e.g., mathematics game), control group is not given anytreatment.
• After 4 months the two-sample t-test is used to compare math scores between the two groups. Each participants is measured once and belongs to one group.
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Tips for data analysis
Leave enough time for data entry and data formatting
• Can take much longer than you expect
Inyour codebook –note the TYPEof variable for each measurement/question
This will allow you to plan the proper levels and types of analysis
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Research Methodology Grouphttps://research.phoenix.edu/content/research-methodology-group
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Reference
Cohen, J. (1992). A power primer. Psychological Bulletin, 112(1), 155–
159. https://doi.org/10.1037/0033-2909.112.1.155
https://statistics.laerd.com/ (Free membership for UOPX Faculty)
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Thank you
Center for Educational and Instructional
Technology Research