1 / 13

Research Methods I

Why Statistics Scientific Method. A systematic, controlled, empirical and critical investigation guided by theoryState problemHypothesisTest relationships empiricallyDraw conclusions. Levels of Measurement. Qualitative vs. QuantitativeCategorical vs. ContinuousNominal vs. interval and rati

kimball
Download Presentation

Research Methods I

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

    1. Research Methods I Review

    2. Why Statistics – Scientific Method ‘A systematic, controlled, empirical and critical investigation guided by theory State problem Hypothesis Test relationships empirically Draw conclusions

    3. Levels of Measurement Qualitative vs. Quantitative Categorical vs. Continuous Nominal vs. interval and ratio Ordinal is qualitative but can be used as continuous (Likert scale) Validity of Measure Content (face, sampling-content), criterion, construct Reliability of Measure Test-retest, inter-rater, internal-consistency

    4. Descriptive Statistics Describe difference between individuals in sample. Frequency distributions (simple and grouped) Graphical Displays Histogram, Stem and Leaf Measures of Central Tendency Mean, Median, Mode Skewness Median smaller than mean – right skewed Median larger than mean – left skewed

    5. Measures of Dispersion How far are individuals away from the mean? (Homogeneous versus heterogeneous samples) Range Interquartile range (middle 50%) Variance S2 = S (X – Mx) / N Standard Deviation Square root of variance, same unit of measurement, greater variability = larger standard deviation Standard deviation and empirical rule +/- 1 SD = 68% Standard scores (z-scores and T-scores) Mean = 0; SD = 1; Z = (X – MX) / s

    6. Linear Statistical Models Regression vs. Correlation Regression – prediction, independent and dependent variable, y = a + bx Correlation – no dependent variable, Pearson correlation coefficient, for non-experimental designs Scatter diagram to display relationship Bivariate frequency distribution Cartesian Coordinates

    7. Correlations Pearson Correlation Coefficient Cross-product: (X – MX) x (Y – MY) Negative cross-product – negative correlation Sum of cross-product (magnitude depends on N) Covariance: Divide sum of cross-product by N Correlation Coefficient Divide covariance by SDX x SDy Correlation and Causation (causal, spurious, reciprocal) Correlation and z-scores (r = S ZX x ZY / N)

    8. Linear Regressions A perfect line: y = a + bx Least Squares Method Residuals: ei = Y – Y (reveal large errors) Sei2 = (Yi – Yi)2 should be as small as possible ayx = MY – byxMx - the y-intercept for this method byx = S (Xi – Mx) ( Yi – My) / S (Xi – Mx)2 Analyze residuals A plot of the residuals will not have random scatter around zero if there is no homoscedasticity Residual analysis can show outliers and other problems Rule of the buldge Coefficient of Determination – R2 (proportion of variance of one variable explained by variance of the other).

    9. Linear Regressions Evaluate Quality of Prediction – Relationship between Y and Y Calculate Y for each X of the sample Calculate the correlation between Y and Y rYY = SCPYY / vSSY x SSY Calculate F for the correlation between Y and Y Partitioning the Y scores (sum of squares) SStotal = SSregression + SSresidual rXY2 = SSregression / SStotal – proportion of total variance that can be accounted for by the independent variable Evaluate Quality of Prediction – Score Model F = MSregression / MSresidual MSregression = SSregression / dfregression

    10. Multiple Regressions Predict score of dependent variable from two or more independent variables Regression plane Y = a + bX + cT Two kinds of multiple regressions Orthogonal (IVs are unrelated to each other) Non-orthogonal (IVs are related to each other)

    11. Orthogonal Regression Assessing quality of prediction Prediction of X plus prediction of T ry.x2 + rY.T2 = RY.XT2 Like in linear regressions SStotal = SSregression + SSresidual Score Model Y = a + bX + cT Y = My + b(X – Mx) + c(T – MT) + (Y – Y)

    12. Introduction to Inferential Statistics Estimate values for whole population State null hypothesis and research hypothesis Decide at which level of significance (a) to reject the null hypothesis (how likely is it that the result was obtained by chance) Less than 5% chance (p < .05) Less than 1% chance (p < .01) Type I and type II error

    13. T-tests One sample t-test When population variance is not known Two sample t-test for independent samples Compare two sample means Samples are independent of each other Two sample t-test for dependent samples Compare two sample means Samples are paired / dependent

More Related