Statistical Processes

¶ … Kolmogorov-Smirnof test Factor analysis Linear regression Goldfeld-Quandt test Kaiser-Meiyer-Oklin (KMO) Multivariate regression Correlation -- Pearson's r Cronbach's ? Durbin-Watson statistic See descriptions and justifications below. Correlation importance and justifications Correlation measures the strengths of association between two variables and, as such, enables the performance of bivariate analysis ("Statistics Solutions, 2012"). The value range of the correlation coefficient extends between +1 and -1. A correlation coefficient of ± 1 indicates a perfect degree of association between the two variables. Assumptions for the Pearson r correlation include normal distribution, linearity, and homoscedasticity ("Statistics Solutions, 2012").

Linearity assumes a straight line relationship between each of the variables in the analysis and homoscedasticity assumes that data is normally distributed about the regression line ("Statistics Solutions, 2012"). 3. Reasoning (justifications) to use parametric or non-parametric statistics Parametric statistics are used when the data is expected to show a type of probability distribution from which inferences can be drawn based on the parameters of that distribution (Geisser & Johnson, 2006).

More assumptions are made when using parametric methods than non-parametric methods, which can generate more precise and accurate estimates if the assumptions are correct; this is known as statistical power (Geisser & Johnson, 2006). 4. Selection of statistical method suitable for the selected model(s) And 5. Justification of the selected statistical method Multivariate analysis is used because there are so many independent variables. This is already discussed in the draft of the paper. 6.

Assumption of the selected statistical method(s) AND 7.Discuss the need of Normality assumption With parametric statistics, there is an assumption that the data will be based on normal probability distributions that have the same shape and are characterized (parameterized) by a mean and standard deviations ("Statistics Solutions, 2012"). That is to say, if the researcher knows the mean and standard deviation -- and if the distribution is, in fact, normal -- then the probability of any future observations can be known ("Statistics Solutions, 2012").

To verify data normality, a goodness of fit test may be used; in this study, the Kolmogorov-Smirnof test will be used ("Statistics Solutions, 2012"). 7. Multicollinearity assumption & implication to student work Multiple linear regression assumes little to no multicollinearity in the data. When independent variables are not independent from each other, multicollinearity exists ("Statistics Solutions, 2012"). There is also an assumption of independence regarding the error of the mean ("Statistics Solutions, 2012"). That is to say that the standard mean error of the dependent variable is independent from the independent variables ("Statistics Solutions, 2012"). 8.

Discuss ways to overcome the Multicollinearity When multicollinearity occurs in the data, centering the data by deducting the mean score may be useful; however, this strategy generally works when the multicollinearity exists due to the application of non-linear transformations that have been used to correct missing multivariate normality ("Statistics Solutions, 2012"). A more robust method is to conduct a factor analysis before running the regression analysis, and then to rotate the factors to insure that the factors are independent in the factor analysis ("Statistics Solutions, 2012"). 9.

Discuss autocorrelation (serial correlation) assumption & implication to student work Autocorrelation (lagged correlation or serial correlation) occurs when the correlation between values in a random process at different times that is a function of the time lag or of the two times ("Statistics Solutions, 2012"). That is to say that there is a relationship between a variable and itself over intervals of time ("Statistics Solutions, 2012"). These serial correlations occur in repeating patterns when the level of a variable at a time certain affects the variable at a future time ("Statistics Solutions, 2012").

10.Discuss ways to overcome the serial correlation When using an estimated equation for statistical inference in hypothesis testing, the residuals will first be examined for evidence of serial correlation ("Statistics Solutions, 2012"). The Durbin-Watson statistic is a first order serial correlation that can be produced as part of the regression output ("Statistics Solutions, 2012"). The Durbin-Watson statistic measures the linear association between adjunct residuals from a regression model. It is basically the test of a the hypothesis p = 0 in the specification: ut = put-1+Et 11.Discuss homoscedasticity.