  Interaction Graphs Statistics Data
 [ CORRELATIONS ] Correlation matrix [ DESCRIPTIVE STATISTICS ] Maximum Mean Minimum N Std Dev [ MODEL ANOVA ] Degrees of freedom F Mean square Significance Sum of squares [ MODEL COEFFICIENTS ] B Significance Std Error t CORRELATIONS :: Correlation Matrix The correlation matrix (presented in columnar format) contains the intercorrelations among all of the variables in the research model. The values reported by Interaction! are Pearson product-moment correlations, which are defined as the covariance of the two variables in question divided by the product of their standard deviations. The correlation values can range from -1 to 1, inclusive, and are reflective of the strength and nature of the linear relationship between the two variables. Return to help index DESCRIPTIVE STATISTICS :: Maximum The value reported for the maximum is the largest value in the dataset for the variable in question. Return to help index DESCRIPTIVE STATISTICS :: Mean The arithmetic mean is a measure of central tendency for the variable in question. It is defined as the sum of all of the valid case scores for the target variable divided by the total number of valid cases for that variable. Return to help index DESCRIPTIVE STATISTICS :: Minimum The value reported for the minimum is the smallest value in the dataset for the variable in question. Return to help index DESCRIPTIVE STATISTICS :: N N refers to the number of valid cases in the dataset for the variable in question. Return to help index DESCRIPTIVE STATISTICS :: Std Dev The standard deviation provides a measure of the variability among the valid case scores for the variable in question. It is defined as the square root of the average of the squares of deviations about the mean of the valid case scores for the target variable. Return to help index INTERACTION LINES :: 95% CI Around the Simple Slope The values reported are the upper and lower confidence limits of a two-tailed 95% confidence interval around the simple slope. You can be 95% certain that the true value of the simple slope in the population for the interaction line in question falls between these values. Return to help index INTERACTION LINES :: Degrees of Freedom The value reported is the degrees of freedom for the significance test of the simple slope for the interaction line in question. This value is equal to the number of valid cases in the dataset minus the number of predictors in the research model minus one. Return to help index INTERACTION LINES :: Intercept The intercept is the point at which the interaction line in question intersects the Y-coordinate axis (i.e., the dependent variable axis). Return to help index INTERACTION LINES :: Level of the Moderator The level of the moderator is the value of the moderator variable that was used to compute the current interaction line. Return to help index INTERACTION LINES :: Moderator The moderator is the variable selected from the dataset that is posited to influence the nature of the relationship between the independent variable and the dependent variable. Different values of the moderator are used to compute the individual interaction lines. Return to help index INTERACTION LINES :: Significance of Simple Slope This value is the probability that the observed relationship between the dependent and independent variables could have occurred by chance alone at the level of the moderator for the interaction line in question. This value is also known as the 'p-value', alpha, and the Type I error rate. By convention this value should be less than 0.05 to claim statistical significance. Return to help index INTERACTION LINES :: Simple Slope This value is a measure of the steepness of the incline or decline of the interaction line in question. It is the regression of the dependent variable on the independent variable at the level of the moderator for the current interaction line. Return to help index INTERACTION LINES :: Standard Error of the Simple Slope This value is the standard error of the regression of the dependent variable on the independent variable at the level of the moderator for the interaction line in question. This value is a function of the variance of the independent variable, the variance of the interaction term, and the covariance of the two. Return to help index INTERACTION LINES :: t This is the Student t-test value used to determine if the regression of the dependent variable on the independent variable at the level of the moderator for the interaction line in question is significantly different from zero. Return to help index MODEL ANOVA :: Degrees of Freedom The regression degrees of freedom is equal to the number of adjustable parameters in the full research model (i.e., the number of predictors). The residual degrees of freedom is equal to the number of valid cases in the dataset minus the number of predictors in the research model minus one. Return to help index MODEL ANOVA :: F The value of the Fisher F-distribution for the full research model. This value is used to compute the model significance, and is equal to the regression mean square divided by the residual mean square. Return to help index MODEL ANOVA :: Mean Square The mean square is an estimate of variance for a source of variation (i.e., regression or residual). For the source of variation in question, the mean square is equal to the sum of squares for that source of variation divided by its corresponding degrees of freedom. Return to help index MODEL ANOVA :: Significance This value is the probability that the observed relationship between the dependent and independent variables in the full research model could have occurred by chance alone. This value is also known as the 'p-value', alpha, and the Type I error rate. By convention this value should be less than 0.05 to claim statistical significance. Return to help index MODEL ANOVA :: Sum of Squares The regression sum of squares is the sum of squares accounted for by the full research model. The residual sum of squares is the sum of squares not accounted for by the full research model. Return to help index MODEL COEFFICIENTS :: B The value reported is the regression coefficient of the dependent variable on the predictor in question. This value represents the rate of change of the dependent variable as a function of changes in the values of the predictor in question. Return to help index MODEL COEFFICIENTS :: Significance The value reported is the significance of the regression coefficient in question. It is the probability that the regression coefficient is statistically equal to zero given that all of the other predictors are included in the research model. By convention, the variable in question can be considered a significant predictor if its significance level is less than 0.05. Return to help index MODEL COEFFICIENTS :: Std Error The value reported is the standard error of the regression coefficient in question. It provides an estimate of the standard deviation of the sampling distribution of the regression coefficient. Return to help index MODEL COEFFICIENTS :: t This is the Student t-test value used to determine if the regression coefficient in question is significantly different from zero. Return to help index MODEL POWER ANALYSIS :: Effect Size (f Square) The value reported is the f Square effect size for multiple regression. It provides a measure of the magnitude of the combined impact of the predictors on the dependent variable. By convention, effect sizes of 0.02, 0.15, and 0.35 are considered small, medium, and large, respectively. Return to help index MODEL POWER ANALYSIS :: Noncentrality Parameter (Lambda) Lambda is the noncentrality parameter of the noncentral F-distribution. It varies as a multiplicative function of the research model's effect size and sample size, and is used in the computation of statistical power. Return to help index MODEL POWER ANALYSIS :: Critical F This is the critical value of the Fisher F-distribution above which the null hypothesis is rejected, given the numerator and denominator degrees of freedom and the significance level. Return to help index MODEL POWER ANALYSIS :: Noncentral F This is the value of the noncentral F cumulative distribution function, given the observed probability level, the noncentrality parameter, and the degrees of freedom. The noncentral F-distribution is a generalization of the F-distribution. Note: The noncentral F value reported by Interaction! is estimated using Laubscher's (1960) square root normal approximation formula for noncentral F. This formula was chosen because it was found to outperform the cube root normal approximation (Cohen and Nee, 1987). Return to help index MODEL POWER ANALYSIS :: Beta (Type II Error Rate) The reported value is the probability of retaining the null hypothesis when the null hypothesis should actually be rejected. Return to help index MODEL POWER ANALYSIS :: Observed Power This value is the probability of rejecting the null hypothesis, given that the null hypothesis is false. By convention, the statistical power should be greater than 0.80. Return to help index MODEL SUMMARY :: R This value is the multiple correlation between the dependent variable and the combined set of predictors. Return to help index MODEL SUMMARY :: R Square This value is the squared multiple correlation for the research model. It indicates the proportion of variance in the dependent variable that is accounted for by the combined set of predictor variables. Return to help index MODEL SUMMARY :: R Square Adjusted This value is a variant of the squared multiple correlation that takes into account the number of predictors in the research model and the total sample size. Return to help index MODEL SUMMARY :: Standard Error of the Estimate This value provides a measure of the predictive efficacy of the full research model. It can also be considered the magnitude of the sampling error. Return to help index MODEL SUMMARY :: R Square Contribution of the Interaction Term This value provides a measure of the increase in the total variance accounted for by the research model due exclusively to inclusion of the interaction term. Return to help index