Statistical Techniques

Statistical analysis is the bridge between raw data and meaningful conclusions. Choosing the correct statistical technique is critical; a wrong choice can invalidate your entire study. This guide breaks down the most common statistical methods used in academic research, helping you select the right tool for your data.

If you are struggling with your analysis or need expert verification, our statistical consulting services can provide the support you need.

Choosing the Right Statistical Test

The choice of test depends on three main factors: the type of data (categorical vs. continuous), the number of groups, and the distribution of data (normal vs. skewed). Use this decision framework:

For a deeper dive into selecting tests, UCLA's IDRE guide is an industry-standard resource.

Comparison Tests: T-Tests and ANOVA

These are the workhorses of experimental research.

The T-Test

Used when comparing the means of exactly two groups.

• Independent Samples T-Test: Compares two separate groups (e.g., Treatment Group vs. Control Group).
• Paired Samples T-Test: Compares the same group at two different times (e.g., Pre-test vs. Post-test).

ANOVA (Analysis of Variance)

Used when comparing the means of three or more groups.

• One-Way ANOVA: Tests if there is a statistically significant difference among the means of three or more independent groups.
• Post-Hoc Tests: If ANOVA finds a significant difference, post-hoc tests (like Tukey or Bonferroni) tell you exactly *which* groups differ.

Regression Analysis

Regression goes beyond correlation; it allows for prediction. It models the relationship between a dependent variable and one or more independent variables.

• Simple Linear Regression: Uses one independent variable to predict a continuous outcome.
• Multiple Linear Regression: Uses multiple independent variables to predict a continuous outcome. It controls for confounding variables.
• Logistic Regression: Used when the outcome is categorical (e.g., Pass/Fail, Buy/Don't Buy).

Understanding regression assumptions (linearity, homoscedasticity, independence) is crucial. Khan Academy's statistics course offers excellent visual explanations of these concepts.

Factor Analysis and Data Reduction

When dealing with large surveys, you often have many correlated variables. Factor analysis reduces these variables into a smaller number of "factors."

• Exploratory Factor Analysis (EFA): Used to discover the underlying structure of a relatively large set of variables.
• Confirmatory Factor Analysis (CFA): Used to verify the factor structure of a set of observed variables.

Non-Parametric Techniques

Real-world data is often messy. It may not follow a normal distribution (the bell curve). In these cases, parametric tests (like t-tests) are invalid.

Non-parametric tests make fewer assumptions about the data.

• Mann-Whitney U Test: The non-parametric alternative to the independent t-test.
• Wilcoxon Signed-Rank Test: The alternative to the paired t-test.
• Chi-Square Test of Independence: Used to determine if there is a significant association between two categorical variables.

Get Help with Your Analysis

Statistical analysis is complex. A single error in test selection or data cleaning can compromise your research. Our team of PhD statisticians can help you choose the right technique, run the analysis in SPSS or R, and write up the results.