Statistical Analysis
Test/Method : Descriptive statistics
Purpose : Summarizes and describes the
main features of a dataset.
Type : Measures of central tendency
(mean, median, mode), Measures of variability (range, variance, standard
deviation), Distribution (skewness, kurtosis), Frequency
Distribution (Frequency tables, Histograms, Bar Charts.)
Assumption: No specific assumptions since
descriptive statistics do not infer beyond the data. - Assumes data is
appropriate for the specific measures (e.g., interval/ratio scale for mean,
variance).
Application : Provides a summary of data
characteristics before conducting inferential statistical analyses. -
Used in initial data exploration to understand the basic structure and
distribution of data. - Helps in identifying outliers, trends, and patterns in
the data. - Commonly applied in reports, presentations, and research
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Test/Method : Chi-square test
Purpose : Tests the association between
categorical variables.
Type : Pearson's Chi-square,
Chi-square for independence, Chi-square for goodness-of-fit
Assumption: Expected frequencies should be
≥ 5 in each cell, independence of observations
Application : Used in contingency tables,
goodness-of-fit tests for categorical data.
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Test/Method : Student t-test
Purpose : Compares the means of two
groups to see if they are significantly different.
Type : Independent samples t-test,
Paired samples t-test, One-sample t-test
Assumption: Normality, equal variances
(for independent t-test), independence of observations.
Application : Comparing means between two
groups (e.g., control vs. treatment).
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Test/Method : ANOVA (Analysis of Variance)
Purpose : Compares means among three or
more groups.
Type : One-way ANOVA, Two-way ANOVA,
Repeated Measures ANOVA
Assumption: Normality, homogeneity of
variance, independence of observations.
Application : Comparing means across
multiple groups or factors.
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Test/Method : Correlation
Purpose : Measures the strength and
direction of a linear relationship between two continuous variables.
Type : Pearson's, Spearman's, Kendall's
Assumption: Linear relationship, normality
(for Pearson's), no significant outliers
Application : Assessing the relationship
between variables (e.g., height and weight).
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Test/Method : Regression
Purpose : Models the relationship
between a dependent variable and one or more independent variables.
Type : Linear Regression, Multiple
Regression, Logistic Regression
Assumption: Linearity, independence,
homoscedasticity, normality of residuals (for linear regression).
Application : Predicting an outcome,
assessing the impact of predictors.
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Test/Method : Multivariate test (MANOVA,
MANCOVA)
Purpose : Tests for differences in multiple
dependent variables across groups (MANOVA), or controlling for covariates
(MANCOVA).
Type : MANOVA, MANCOVA
Assumption: Multivariate normality,
homogeneity of variance-covariance matrices, independence of observations.
Application : Examining group differences on
multiple outcomes, adjusting for covariates.
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Test/Method : Validity Test (Factor
analysis)
Purpose : Reduces data to a smaller set
of underlying factors, tests construct validity.
Type : Exploratory Factor Analysis
(EFA), Confirmatory Factor Analysis (CFA)
Assumption: Adequate sample size,
linearity, Multicollinearity, normality.
Application : Identifying underlying
constructs, assessing the validity of measurement instruments.
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Test/Method : Reliability Test (Cronbach’s
alpha)
Purpose : Assesses the internal consistency
of a set of items or scale.
Type : Cronbach's Alpha
Assumption: Items should measure the same
underlying construct, appropriate for continuous/ordinal data.
Application : Evaluating the reliability of
a survey or test.
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Test/Method : Friedman Rank test
Purpose : Non-parametric alternative to
the repeated measures ANOVA; compares ranks across multiple groups.
Type : Friedman Test
Assumption: Requires the data to be
ordinal or interval, blocks of data should be comparable.
Application : Used when the assumptions of
repeated measures ANOVA are not met, analyzing ranked data.
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Test/Method : Structure Equation Modelling
(SEM)
Purpose : Analysis complex relationships
between observed and latent variables; includes measurement and structural
models.
Type : SEM, Path Analysis,
Confirmatory Factor Analysis (CFA)
Assumption: Large sample size, normality,
no multicollinearity, appropriate model specification.
Application : Modelling complex
relationships between variables, used in social sciences, psychology, etc.
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