4 SAMPLING DISTRIBUTION OF THE MEAN Chapter
1. Sampling Methods . . . . . . . . . . . . . . . . . . . . . . . . . . .118 a. Non-probabilitySampling........................119 i. PurposiveSampling.........................119 ii. Convenience Sampling . . . . . . . . . . . . . . . . . . . . . .119 iii. QuotaSampling............................119 b. ProbabilitySampling............................120 i. Simple Random Sampling . . . . . . . . . . . . . . . . . . . .120 ii. Systematic Random Sampling. . . . . . . . . . . . . . . . .121 iii. Stratified Random Sampling . . . . . . . . . . . . . . . . . .121 iv. Cluster Random Sampling. . . . . . . . . . . . . . . . . . . .121 v. Multistage Random Sampling . . . . . . . . . . . . . . . . .121 2. Sample Size Determination . . . . . . . . . . . . . . . . . . . .121 3. Sampling Distribution of the Sample Means. . . . . . . .125 4. Central Limit Theorem. . . . . . . . . . . . . . . . . . . . . . . . .127 1. Point Estimates and Interval Estimates . . . . . . . . . . .142 a. Point Estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .142 b. Interval Estimate and Confidence Interval ...........143 i. Confidence Interval Estimation for Large Samples . . . . . . . . . . . . . . . . .144 ii. Confidence Interval Estimation for Small Samples . . . . . . . . . . . . . . . . .147 iii. Confidence Interval Estimation for Proportion . . . . . . . . . . . . . . . . . . . . .151 iv. Finite Population Correction Factor . . . . . . . . . . . . .153 2. HypothesisTesting ...........................154 3. Statistical Hypothesis Testing Procedure . . . . . . . . . .155 a. Null Hypothesis and Alternative Hypothesis. . . . . . . . . .156 b. One-Tailed Test and Two-Tailed Test ...............157 c. Level of Significance ............................157 d. Type I Error and Type II Error. . . . . . . . . . . . . . . . . . . . .158 e. TestStatistic..................................158 f. Decision Rule: Critical Value Approach . . . . . . . . . . . . .158 g. Decision Rule: p -valueApproach..................159 4. Approaches to Hypothesis Testing . . . . . . . . . . . . . . .159 a. Hypothesis Test about a Population Mean (One-Sample, z Test) . . . . . . . . . . . . .159 b. Hypothesis Test about a Population Mean (One-Sample, t Test) . . . . . . . . . . . . .163 c. Hypothesis Test about a Proportion (One-Sample, z Test) . . . . . . . . . . . . . . . . . .168 d. Hypothesis Test about a Population Mean (Independent Two-Sample, z Test).................169 e. Hypothesis Test about a Population Mean (Independent Two-Sample, t Test) ...172 f. Hypothesis Test about a Proportion (Two-Sample, t Test)...................174 5. Software Application in Inferential Statistics . . . . . . . .176 a. Hypothesis Test for a Population Mean (Independent Two-Sample, Equal and Unequal Variances, t Test) . . . . . . . . . . . . . .177 b. Hypothesis Test for a Population Mean (Dependent Two-Sample, Paired Sample, t Test) . . . . .179 1. The F Distribution and Analysis of Variance (ANOVA) .........................194 a. Comparing Two Population Variances ( F Test) .......195 b. Analysis of Variance (ANOVA) Test . . . . . . . . . . . . . . . .199 c. Inferences about Pairs of Treatment Means. . . . . . . . . .203 2. The Chi-Square Distribution and Nonparametric Hypothesis Testing . . . . . . . . . . . . . .205 a. Characteristics of the Chi-Square Distribution . . . . . . . .206 b. Chi-Square Test Statistic and Analysis. . . . . . . . . . . . . .206 c. Chi-Square Goodness-of-Fit Test: Equal Expected Frequencies . . . . . . . . . . . . . . . . . . . . .207 d. Chi-Square Goodness-of-Fit Test: Unequal Expected Frequencies. . . . . . . . . . . . . . . . . . .209 e. Chi-Square Test of Independence: Contingency Table Analysis . . . . . . . . . . . . . . . . . . . . . .211 f. Kruskal-Wallis H Test ...........................214 g. Kendall W Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .217 h. Mann-Whitney U Test...........................220 i. Wilcoxon Signed-Rank Test (for Related Samples) . . . .226 3. Test for Normality . . . . . . . . . . . . . . . . . . . . . . . . . . . .229 a. Jarque-Bera Test for Normality. . . . . . . . . . . . . . . . . . . .230 b. Kolmogorov-Smirnov Test for Normality. . . . . . . . . . . . .232 1. CorrelationAnalysis ..........................251 Dependent and Independent Variables. . . . . . . . . . . . . . . . .253 2. The Correlation Coefficient . . . . . . . . . . . . . . . . . . . . .255 a. Pearson’s Correlation Coefficient . . . . . . . . . . . . . . . . .255
STATISTICAL ANALYSIS WITH SOFTWARE APPLICATIONS h. Mann-Whitney U Test...........................220 i. Wilcoxon Signed-Rank Test (for Related Samples) . . . .226 3. Test for Normality . . . . . . . . . . . . . . . . . . . . . . . . . . . .229 a. Jarque-Bera Test for Normality. . . . . . . . . . . . . . . . . . . .230 b. Kolmogorov-Smirnov Test for Normality. . . . . . . . . . . . .232
7 CORRELATION AND REGRESSION ANALYSIS Chapter
5 INFERENTIAL STATISTICS Chapter
1. CorrelationAnalysis ..........................251 Dependent and Independent Variables. . . . . . . . . . . . . . . . .253 2. The Correlation Coefficient . . . . . . . . . . . . . . . . . . . . .255 a. Pearson’s Correlation Coefficient . . . . . . . . . . . . . . . . .255 b. Spearman’s Rank Correlation Coefficient ...........257 3. Correlation and Causation . . . . . . . . . . . . . . . . . . . . .260 4. RegressionAnalysis..........................262 Least Squares Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . .262 5. SimpleLinearRegression......................263 a. Assumptions of Simple Linear Regression. . . . . . . . . . .264 b. Estimating the Coefficients of Simple Linear Regression Model . . . . . . . . . . . . . . . . . .265 c. Estimating the Standard Error . . . . . . . . . . . . . . . . . . . .267 d. Constructing the Confidence and Prediction Intervals. . . . . . . . . . . . . . . . . . . . . . . . . . . . .268 e. Coefficient of Determination ......................270 f. Relationship of Correlation Coefficient, Standard Error of Estimate, and Coefficient of Determination ......................271 6. Multiple Linear Regression. . . . . . . . . . . . . . . . . . . . .272 a. Assumptions of Multiple Linear Regression. . . . . . . . . .273 b. Estimating the Coefficients of the Multiple Linear Regression Model . . . . . . . . . . . . . . . . .274 c. Interpreting the Multiple Linear Regression . . . . . . . . . .275 7. Regression Analysis with Dummy Variables. . . . . . . .280 8. Positive Monotonic Transformation of Data . . . . . . . .282 9. Modeling Relationships of Multiple Variables with Linear Regression . . . . . . . . . . . . . . . .284 10. Advanced Regression Models . . . . . . . . . . . . . . . . . .286 Appendices ...................................297 1. List of Statistical Tables. . . . . . . . . . . . . . . . . . . . . . . .297 a. Cumulative Normal Distribution . . . . . . . . . . . . . . . . . . .297 i. Table of Standard Normal Probabilities for Negative Z -scores . . . . . . . . . . . . . . . . . . . . . . . .297 ii. Table of Standard Normal Probabilities for Positive Z -scores . . . . . . . . . . . . . . . . . . . . . . . . .297 b. Critical Values of the t Distribution . . . . . . . . . . . . . . . . .297 c. Critical Values of the F Distribution.................297 i. Critical Values of F at the 5% Significance Level . . .297 ii. Critical Values of F at the 1% Significance Level . . .297 iii. Critical Values of F at the 0.1% Significance Level ...........................297 d. Critical Values of the Chi-Square Distribution. . . . . . . . .297 e. Critical Values of the Mann-Whitney U ..............297 f. Critical Values of the Wilcoxon Signed-Rank Test . . . . .297 g. Critical Values of the One Sample Kolmogorov-Smirnov Test of Normality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .297 h. Critical Values for the Spearman’s Rank Correlation Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . .297 2. Appendix 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .298 3. Appendix 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .299 4. Appendix 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .300 5. Appendix 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .306 6. Appendix 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .307 7. Appendix 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .308 8. Appendix 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .309 9. Appendix 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .310 10. Appendix 9: Rubric for Grading Concept Map and Essay Questions . . . . . . . . . . . . . . . . . . . . . . . . .311 11. Sample Datasets. . . . . . . . . . . . . . . . . . . . . . . . . . . . .312 a. World/International.............................312 b. Philippines/Local . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .312 Index ........................................314 Worksheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .322
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