1. Analyzing and Interpreting Quantitative Data
Chapter 6
Analyzing and Interpreting Quantitative Data
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2. By the end of this chapter, you should be able to:
Identify the steps in the process of analyzing and interpreting quantitative data
Describe the process of preparing your data for analysis
Identify the procedures for analyzing your data
Learn how to report the results of analyzing your data
Describe how to interpret the results

3. Steps in the Process of Quantitative Data Analysis
Preparing the data for analysis
Conducting the data analysis
Reporting the results
Interpreting the results

4. Preparing the Data for Analysis: Inputting Data
Score data by assigning numeric codes to responses
Create a codebook
Use information from instruments when possible as a part of coding scheme
Create a data file in data grid
Create variable, value labels
Clean database, missing values

5. Determine Types of Scores to Analyze
Single item
Summed scores
Difference scores

6. Selecting a Statistical Program
Statistical Package for Social Sciences (SPSS) most popular
Other programs
Minitab
JMP
SYSTAT
SAS

7. Conducting Descriptive Analysis
Measures of central tendency (value or score that represents the entire distribution)
Mean: Typically called the “average”
Median: The value or score that divides the top half of a distribution from the bottom half
Mode: The value or score that occurs most often
Measures of variability (describes the “spread” of the scores
Range: The difference between the highest and lowest scores
Standard deviation: The standard distance the scores are away from the mean

8. Conducting Descriptive Analysis
Measures of relative standing
Percentile rank: The percentage of participants in the distribution with scores at or below a particular score
Calculated score: Enables a researcher to compare scores from different scales
Z-Score: A popular form of the standard score, has a mean of 0 and a standard deviation of 1

9. Descriptive Statistics
Central Tendency
Variability
Relative Standing
Mean
Median
Mode
Variance
Standard Deviation
Range
Z-Score
Percentile Ranks

10. Inferential Statistics
Analysis of
Variance
Chi-Square
Pearson
Correlation
Multiple
Regression
T-test

11. Conducting Inferential Analysis
Hypothesis testing: A procedure for making decisions about results by comparing an observed value of a sample with a population value to determine if no difference or relationship exists between the values
Confidence interval: The range of upper and lower statistical values that is consistent with observed data and is likely to contain the actual population mean

12. Conducting Inferential Analysis (cont’d)
Effect size: A means for identifying the practical strength of the conclusions about group differences or about the relationship among variables

13. Conducting Hypothesis Tests
Identify a null and alternative hypothesis
Set the level of significance (alpha level) for rejecting the null hypothesis
Collect the data
Compute the sample statistic
Make a decision about rejecting/failing to reject

14. Selecting an Appropriate Statistic
Determine the type of quantitative research question or hypothesis you want to analyze
Identify the number of independent variables
Identify the number of dependent variables
Identify whether covariates and the number of covariates are used in the research question or hypothesis

15. Selecting an Appropriate Statistic
Consider the scale of measurement for your independent variable(s) in the research question or hypothesis
Identify the scale of measurement for the dependent variables (e.g., continuous or categorical)
Determine if the distribution of the scores is normal or skewed

16. Normal Curve 34% 34% 13.5% 13.5% 2.5% 2.5% Mean -3 -2 -1 +1 +2 +3
Standard Deviations

17. The Normal Curve of Mean Differences of All Possible Outcomes If the Null Hypothesis Is True
Reject the
Null
Hypothesis
Reject the
Null
Hypothesis
High Probability
Values If the Null
Hypothesis Is True
Extremely Low
Probability Values
If Null Hypothesis
Is True (Critical
Region)
Extremely Low
Probability Values
If Null Hypothesis
Is True (Critical
Region)
Alpha=.025
Alpha=.025
Two-Tailed Test

18. Outcomes of Hypothesis Testing: Type I and Type II Errors
Decision Made by
the Researcher
Based on the
Statistical Test
Value
State of Affairs in the Population
No Effect:
Null True
Effect Exists:
Null False
Type I Error
(false positive)
(probability =
Alpha)
Correctly
rejected:
no error
(probability =
power)
Reject the
Null
Hypothesis
Correctly not
rejected:
no error
Type II Error
(false negative)
(probability =
Beta)
Fail to Reject the
Null Hypothesis

19. Reporting the Results Tables summarize statistical information
Title each table
Present one table for each statistical test
Organize data into rows and columns with simple and clear headings
Report notes that qualify, explain, or provide additional information in the tables, which can be helpful to readers. Notes include information about the size of the sample reported in the study, the probability values used in hypothesis testing, and the actual significance levels of the statistical test

20. Reporting the Results (cont’d)
Figures (charts, pictures, drawings) portray variables and their relationships
Labeled with a clear title that includes the number of the figure
Augment rather than duplicate the text
Convey only essential facts
Omit visually distracting detail
Easy to read and understand
Consistent with and are prepared in the same style as similar figures in the same article
Carefully planned and prepared

21. Reporting the Results (cont’d)
Detailed explanations about statistical results
Report whether the hypothesis test was significant or not
Provide important information about the statistical test, given the statistics
Include language typically used in reporting statistical results

22. Discussing the Results
Summarize major results
Explain why they occurred
Explain the implications of the results for the audiences
Advance limitations
Suggest future research
End on positive note