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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.
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DESCRIPTIVE STATISTICS :: Maximum
The value reported for the maximum is the largest value in the
dataset for the variable in question.
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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.
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DESCRIPTIVE STATISTICS :: Minimum
The value reported for the minimum is the smallest value
in the dataset for the variable in question.
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DESCRIPTIVE STATISTICS :: N
N refers to the number of valid cases in the dataset for the variable
in question.
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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.
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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.
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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.
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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).
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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MODEL COEFFICIENTS :: t
This is the Student t-test value used to determine if the
regression coefficient in question is significantly different from zero.
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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.
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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.
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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.
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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).
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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.
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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.
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MODEL SUMMARY :: R
This value is the multiple correlation between the dependent variable
and the combined set of predictors.
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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.
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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.
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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.
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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.
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