Chapter 8 Analyzing and Interpreting Quantitative Data Educational

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

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

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

Explore and Analyze the Data • 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 • Calculate descriptive statistics • Measures of central tendency • Measures of variability • Measures of relative standing Educational Research by John W. Creswell. Copyright © 2002 by Pearson Education. All rights reserved. Slide 4

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

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

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

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

Normal Curve 34% 13. 5% 2. 5% -3 2. 5% -2 -1 Mean Standard Deviations Educational Research by John W. Creswell. Copyright © 2002 by Pearson Education. All rights reserved. Slide 9 +1 +2 +3

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

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

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

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

Analyze Data for Hypothesis Testing: Factors to Consider • 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 Educational Research by John W. Creswell. Copyright © 2002 by Pearson Education. All rights reserved. Slide 14

Analyze Data for Hypothesis Testing: Factors to Consider • 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 Educational Research by John W. Creswell. Copyright © 2002 by Pearson Education. All rights reserved. Slide 15

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

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

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

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