Kegunaan Statistik Bivariat dan Multivariat dalam Penelitian Korelasional

TYPES OF MULTIVARIATE CORRELATIONAL STATISTICS

Statistic	Use
Canonical correlation	For determining the correlation between a set of criterion variables and a set of predictor variables
Differential analysis	For comparing correlation coefficients obtained from homogeneous subgroups within a sample, can be used to identify moderator variables that improve a measure’s predictive validity
Discriminant analysis	For determining the correlation between a set predictor variables and a criterion variable that is in the form of categories
Factor analysis	For reducing a large number of variables to a small number of factors, with each factor representing a set of variables that are moderately or highly correlated with each other
Hierarchical linear regression	For examining the correlation between a set of predictor variables and a criterion variable at different units of statistical analysis, for example the relationship between student characteristics and academic achievement at the teacher level, school level, and district level
Logistic regression	For determining the correlation between a dichotomous criterion variable and a set of predictor variables
Multiple linear regression	For determining the correlation between a criterion variable and set of predictor variables
Nonlinear regression	For determining the correlation between a criterion variable and a set of predictor variables when the correlations are hypothesized to be linear
Path analysis	For testing theories about the hypothesized causal links between a set of variables
Poisson regression	For determining the correlation between a set of predictor variables and a criterion variable that is in the form of a frequency count
Structural equation modelling	For testing theories about hypothesized causal links between variables, yield more valid and reliable measure of the variables to be analyzed than does path analysis
Time series analysis	For determining whether changes in the data collected on a time-ordered variable (example variable in which the data can be arranged in chronological order) are chance occurrences or the effect of some intervention

BIVARIATE CORRELATIONAL STATISTICS

Technique	Symbol	Variable 1	Variable 2	Remarks
Product moment correlation	r	Continuous	Continuous	The most stable technique, smallest standard error
Rank difference correlation (rho)		Ranks	Ranks	A special form of product-moment correlation
Kendall’s tau		Ranks	Ranks	Preferable to rho for samples less than 10
Biserial correlation	rbis	Artificial dichotonomy	Continuous	Values can exceed 1, has a larger standard error than r, commonly used in item analysis
Widespread biserial correlation	rwbis	Widespread artificial dichotonomy	Continuous	Used when the researcher is interested in persons at the extremes on the dichotonomized variable
Point biserial correlation	rpbis	True dichotonomy	Continuous	Yields a lower correlation than rbis
Tetrachoric correlation	rt	Artificial dichotonomy	Artificial dichotonomy	Used when both variables can be split at critical points
Phi coefficient		True dichotonomy	True dichotonomy	Used in calculating inter item correlations
Contingency coefficient		Two or more categories	Two or more categories	Comparable to rt under certain conditions, closely related to chi-square
Correlation ratio, eta	ƞ	Continuous	Continuous	Used to detect nonlinear relationship