Chapter 7 Analyzing and Interpreting Quantitative Data Power

Chapter 7 Analyzing and Interpreting Quantitative Data Power Point Slides by Ronald J. Shope in collaboration with John W. Creswell

Steps in quantitative analysis and interpretation • How do you analyze the data? • How do you report the results? • How do you discuss the results? Educational Research 2 e: Creswell

How do you analyze the data? Conduct descriptive analysis • Conduct descriptive analysis – Measures of central tendency – Measures of variability – Measures of relative standing Educational Research 2 e: Creswell

Run Descriptive statistics Descriptive Statistics Central Tendency Variability Mean Median Mode Relative Standing Variance Z-Score Standard Deviation Percentile Ranks Range Educational Research 2 e: Creswell

Conduct inferential analysis • Hypothesis testing Educational Research 2 e: Creswell

Conduct hypothesis tests • Identify a null and alternative hypothesis • Set the level of significance (alpha level) for rejecting the null hypothesis • collect data • Compute the sample statistic • Make a decision about rejecting/failing to reject Educational Research 2 e: Creswell

Computing the sample statistic Inferential Statistics Continuous (iv) Continuous (dv) Continuous (iv)Continuous (dv) Chi-Square Parametric Nonparametric Analysis Pearson Correlation Coefficient Regression Coefficient T-Test Spearman Rho Analysis of Kendall’s Variance Tau Analysis of Covariance Mann- Discriminant Point Witney Analysis Biserian U-Test Correlation Kruskall Wallis Test Friedman Two-Way Anova Educational Research 2 e: Creswell Phi Coefficient

Normal Curve 34% 13. 5% 2. 5% -3 2. 5% -2 Mean +1 -1 Standard Deviations Educational Research 2 e: Creswell +2 +3

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 is True (Critical Two-Tailed Test Region) Educational Research 2 e: Creswell Reject the Null Hypothesis Extremely low Probability Values if Null Hypothesis is True (Critical Region)

Outcomes of hypothesis testing: Type I and type II errors Decision made by the Researcher Based on the Statistical Test Value Reject the Null Hypothesis Fail to Reject the Null Hypothesis State of Affairs in the Population No Effect. Null True Type I Error (false positive) (probability= Alpha) Correctly not rejected no error Educational Research 2 e: Creswell Effect Exists Null False Correctly rejected no error (probability= power) Type II Error (false negative) (probability= Beta)

How do you report the results? • Tables summarize statistical information • Figures (charts, pictures, drawings) portray variables and their relationships • Detailed explanations about statistical results Educational Research 2 e: Creswell

How do you discuss the results? • • Summarize major results Explain why they occurred Advance limitations Suggest future research Educational Research 2 e: Creswell