 Data analysis
quantitative/qualitative approach; univariate/multivariate; parametric/nonparametric/robust test;
Data analysis involves examining and interpreting data to extract meaningful insights. Univariate and multivariate tests are two types of statistical analyses used to explore different aspects of data. Let’s take a closer look at each:

 Univariate Analysis:
Definition: Univariate analysis focuses on examining a single variable at a time. It helps in understanding the distribution and characteristics of individual variables.  Common Techniques:
Descriptive Statistics: Measures like mean, median, mode, range, and standard deviation provide a summary of the distribution of a single variable.
Descriptive – MCT (mean, mode, median), MV (variance, standard deviation, Coefficient of variation, skewness, kurtosis, IQ, quantile…
• Data visualization – graphs, bars. charts, QQ plots, PP plots, Box and plots, histograms, scatter, residual plots
• Transformation data – X3 (cube),X2 (square),(square root),X0 (?log), reciprocal root, reciprocal,reciprocal square
• Variety of sampling distribution – testing
 Univariate Analysis:
 Inferential Statistics: Techniques like ttests, ANOVA (Analysis of Variance), and chisquare tests are used to make inferences about the population based on sample data.
Example: If you are studying the heights of a group of individuals, univariate analysis would involve looking at the distribution of heights, calculating measures like the average height, and conducting tests to compare the heights of different subgroups.
Tests: parametric/nonparametric/robust
1. One sample, independent sample, and related sample Ttest
2. ANOVA (oneway, twoway;n way; factorial; post hoc),
3. Linear and non linear correlation
4. Chi square test (qualitative data)
5. Loglinear (qualitative data)
6.Logit and probit, ridge, quantile…nonlinear regression
7. ANCOVA
 Multivariate Analysis:
Definition: Multivariate analysis involves the simultaneous analysis of multiple variables to understand the relationships and patterns among them.
Common Technique  Multivariate Analysis of Variance (MANOVA): Extends ANOVA to multiple dependent variables.
• Principal Component Analysis (PCA): Reduces the dimensionality of data while preserving most of its variability.
• Canonical Correlation Analysis (CCA): Examines the relationship between two sets of variables.
• Multiple Regression Analysis: Examines the relationship between a dependent variable and multiple independent variables.
• Mediation and moderation (SEM); full mediation, partial mediation, recursive and non recursive, CFA, EFA
• Path analysis
• ANCOVA – Analysis of covariance (general linear model)
• MANCOVA – Multivariate Analysis of covariance
• Discriminative analysis
• Factorial; MANOVA, MANCOVA
• Longitudinal Canonical Correlation Analysis (LCCA)
• RASCH measurement theory
Example: If you are studying the factors influencing academic performance, multivariate analysis might involve considering variables like study hours, attendance, and extracurricular activities simultaneously to understand their combined impact on grades.

 When to Use Each:
Univariate Analysis: Useful for understanding the characteristics of individual variables and making comparisons between groups for a single variable.
Multivariate Analysis: Appropriate when exploring relationships between multiple variables and understanding complex patterns in the data.  Software Tools:
Univariate Analysis: Can be performed using tools like Excel, SPSS, or R.
Multivariate Analysis: Requires more advanced statistical software like SPSS, R, Python.AMOS, Mon Carlo (using libraries like NumPy, SciPy, and scikitlearn), or specialized software for specific technique.
 When to Use Each:

 In summary, both univariate and multivariate analyses play crucial roles in data analysis, and the choice between them depends on the research questions and the nature of the data you are working with.
Statistical inference
Testing a hypothesis (experimental/quasiexperimental research design)
Bayesian inference (posterior probability); Bias
Bootstrapping procedures (re sampling by iteration)
Posterior probability
 In summary, both univariate and multivariate analyses play crucial roles in data analysis, and the choice between them depends on the research questions and the nature of the data you are working with.