1. Educational Research by John W. Creswell. Copyright © 2002 by Pearson Education. All rights reserved. Slide 1 Chapter 8 Analyzing and Interpreting Quantitative Data

2. Educational Research by John W. Creswell. Copyright © 2002 by Pearson Education. All rights reserved. Slide 2 The Process of Analysis and Interpretation 4 Prepare and organize the data for analysis 4 analyze the data to explore and describe it 4 analyze the data to test hypotheses (or research questions) 4 Represent or summarize the data in tables, figures including a detailed discussion 4 Conclude the results by summarizing key findings

3. Educational Research by John W. Creswell. Copyright © 2002 by Pearson Education. All rights reserved. Slide 3 Preparing and Organizing the Data 4 Assign numeric scores to the data 4 Consider what types of scores to use –single item –summed on a scale –difference 4 Select a statistical program 4 Input the data

4. Educational Research by John W. Creswell. Copyright © 2002 by Pearson Education. All rights reserved. Slide 4 Explore and Analyze the Data 4 Clean and account for missing data –visually inspect for missing scores –run a frequency distribution to see if any scores are outside the coded range 4 Calculate descriptive statistics –Measures of central tendency –Measures of variability –Measures of relative standing

5. Educational Research by John W. Creswell. Copyright © 2002 by Pearson Education. All rights reserved. Slide 5 Examples of the Family of Statistics in Educational Research Descriptive Statistics Central Tendency VariabilityRelative Standing Mean Median Mode Variance Standard Deviation Range Z-Score Percentile Ranks

6. Educational Research by John W. Creswell. Copyright © 2002 by Pearson Education. All rights reserved. Slide 6 Explore and Analyze the Data 4 Calculate inferential statistics 4 Determine the distribution of the scores –Normal distribution –Skewed distribution –Kurtosis distribution

7. Educational Research by John W. Creswell. Copyright © 2002 by Pearson Education. All rights reserved. Slide 7 The Process of Quantitative Data Analysis The Process: Decisions to be made: Reasons for Decision: Procedures: Exploring and Describing the Data To clean the data base and substitute missing data To see if the data are normally distributed To describe trends in the data To address descriptive questions To remove errors and address missing data Inspect data and insert missing values To determine the type of statistics to use in testing To obtain a general sense of results To obtain results to descriptive questions Run frequency distribution and statistics, check for skewness and kurtosis, and normal distribution

8. Educational Research by John W. Creswell. Copyright © 2002 by Pearson Education. All rights reserved. Slide 8 Identifying trends and addressing research questions 4 Generate a frequency distribution to determine if the scores fall into a normal distribution or if they are skewed 4 Use descriptive statistics to address trends and to address descriptive research questions

9. Educational Research by John W. Creswell. Copyright © 2002 by Pearson Education. All rights reserved. Slide 9 Normal Curve 34% 13.5% 2.5% Standard Deviations Mean +1 +2+3-2-3

10. Educational Research by John W. Creswell. Copyright © 2002 by Pearson Education. All rights reserved. Slide 10 Skewness 4 3 2 1 0 Percentages Negative Skewness 4 3 2 1 0 Positive Skewness Percentages

11. Educational Research by John W. Creswell. Copyright © 2002 by Pearson Education. All rights reserved. Slide 11 Kurtosis 4 3 2 1 0 Percentages Negative Kurtosis 4 3 2 1 0 Positive Kurtosis Percentages

12. Educational Research by John W. Creswell. Copyright © 2002 by Pearson Education. All rights reserved. Slide 12 Examples of the Family of Statistics in Educational Research Inferential Statistics Parametric Nonparametric Parametric Nonparametric Parametric Chi-Square Analysis Phi Coefficient Pearson Correlation Coefficient Regression Coefficient Spearman Rho Kendall’s Tau Continuous (iv) Continuous (dv) Continuous (iv)- Continuous (dv) Continuous (iv)- Continuous (dv) Continuous (iv)- Continuous (dv) T-Test Analysis of Variance Analysis of Covariance Mann- Witney U-Test Kruskall Wallis Test Friedman Two-Way Anova Discriminant Analysis Point Biserian Correlation

13. Educational Research by John W. Creswell. Copyright © 2002 by Pearson Education. All rights reserved. Slide 13 The Process of Quantitative Data Analysis The Process: Decisions to be made: Reasons for Decision: Procedures: Conducting statistical Tests To choose a statistic To test hypotheses To learn about the magnitude of effects and estimate the range of scores To select a statistic that meets criteria Consider statistics and assess criteria To determine if scores are statistically significant To determine the magnitude of differences, relationships, effects and range of scores Conduct six steps of hypothesis testing Assess effect size Estimate confidence intervals

14. Educational Research by John W. Creswell. Copyright © 2002 by Pearson Education. All rights reserved. Slide 14 Analyze Data for Hypothesis Testing: Factors to Consider 4 Determine the type of quantitative research question or hypothesis you want to analyze 4 Identify the number of independent variables 4 Identify the number of dependent variables 4 Identify whether covariates and the number of covariates are used in the research question or hypothesis

15. Educational Research by John W. Creswell. Copyright © 2002 by Pearson Education. All rights reserved. Slide 15 Analyze Data for Hypothesis Testing: Factors to Consider 4 Consider the scale of measurement for your independent variable (s) in the research question or hypothesis 4 Identify the scale of measurement for the dependent variables (e.g. continuous or categorical) 4 Determine if the distribution of the scores is normal or skewed

16. Educational Research by John W. Creswell. Copyright © 2002 by Pearson Education. All rights reserved. Slide 16 Conduct Hypothesis Testing 4 Establish a null and alternative hypothesis 4 set the level of significance (alpha level) for rejecting the null hypothesis 4 collect data 4 compute a simple statistic using a computer 4 decide to accept or reject the null hypothesis 4 Determine if statistically significant differences exist

17. Educational Research by John W. Creswell. Copyright © 2002 by Pearson Education. All rights reserved. Slide 17 The Normal Curve of Means Differences of All Possible Outcomes if the Null Hypothesis is True Reject the Null Hypothesis Reject the Null Hypothesis Extremely low Probability Values if Null Hypothesis is True (Critical Region Alpha=.025 Extremely low Probability Values if Null Hypothesis is True (Critical Region Alpha=.025 Two-Tailed Test High Probability Values if the Null Hypothesis is True

18. Educational Research by John W. Creswell. Copyright © 2002 by Pearson Education. All rights reserved. Slide 18 Type I and Type II Error State of Affairs in the Population Decision made by the Researcher Based on the Statistical Test Value Type I Error (false positive) (probability= alpha Correctly not rejected no error Correctly rejected no error (probability= power) Type II Error (false negative) (probability= beta Reject the Null Hypothesis No Effect- Null True Effect Exists Null False Fail to Reject the Null Hypothesis

19. Educational Research by John W. Creswell. Copyright © 2002 by Pearson Education. All rights reserved. Slide 19 Representing and Reporting Results 4 Tables summarize statistical information 4 Figures (charts, pictures, drawings) portray variables and their relationships 4 Detailed explanations about statistical results