Basic Statistical Concepts
📌 Statistical methods are divided into two main types: descriptive statistics (used for data presentation like tables/graphs and calculating measures like mean, median, mode, standard deviation, and variance) and inferential statistics (used for drawing comprehensive conclusions about a population based on sample data).
📊 Descriptive statistics helps in understanding data characteristics, while inferential statistics is crucial for making decisions based on samples.

Types of Statistical Data
📌 Data types determine the appropriate statistical test:
1. Nominal Data: Categorical data without inherent order (e.g., gender coded as 1 or 2); numerical codes are only for identification and cannot be used in mathematical operations.
2. Ordinal Data: Categorical data with a meaningful order or rank (e.g., education levels coded 1 to 4 or satisfaction ratings); these codes cannot be mathematically operated on (like division).
3. Interval Data: Data possessing specific intervals or distances between measurements (e.g., temperature in degrees Celsius); it's a higher level than ordinal data.
4. Ratio Data: The highest level of data, representing true numerical quantities where all mathematical operations (addition, subtraction, multiplication, division) are valid (e.g., the actual count of items, like 24 or 27 loaves of bread).

Parametric vs. Non-Parametric Statistics
📌 The choice between parametric and non-parametric tests depends on data characteristics and sample size:
⚖️ Parametric Statistics require two main conditions: the data must follow an interval or ratio scale, AND the data must be normally distributed (verified via a normality test).
🎲 Non-Parametric Statistics are used when data is nominal or ordinal, or when interval/ratio data fails the normality test, especially with small sample sizes (e.g., $n < 30$).

Choosing the Right Statistical Test (By Research Design)
📌 Specific tests are selected based on the research objective and sample structure:
1. One Sample Test: Used to compare the sample mean against a known population mean.
* Parametric options: T-Test (One Sample T-Test) or Z-Test.
* Non-Parametric options: Binomial Test or Kolmogorov-Smirnov Test.
2. Two Related Samples (Paired): Used to test differences within the same subjects under two different treatments.
* Parametric options: Paired Samples T-Test or Z-Test.
* Non-Parametric options: Wilcoxon Signed-Rank Test or McNemar Test.
3. Two Unrelated Samples: Used to compare the means of two independent populations.
* Parametric options: Independent Samples T-Test (requires both Normality and Homogeneity of Variance tests).
* Non-Parametric options: Mann-Whitney U Test or Median Test.
4. Multiple Related Samples:
* Non-Parametric options: Friedman Test.
5. Multiple Unrelated Samples:
* Parametric options: F-Test and T-Test (if data is normally distributed).
* Non-Parametric options: Kruskal-Wallis Test or $\chi^2$ (Chi-Square) Test.
6. Correlation/Relationship Between Variables:
* Tests include Pearson correlation or Kendall's correlation.

Key Points & Insights
➡️ Before choosing a statistical test, always determine the data type (Nominal, Ordinal, Interval, Ratio), as this heavily influences the subsequent test selection.
➡️ For interval/ratio data, normality testing is mandatory before proceeding to parametric tests like the T-Test or Z-Test.
➡️ If sample size is very small (e.g., $n=5$ or $n=9$), consider using non-parametric tests immediately without performing the normality test.
➡️ For two unrelated samples using parametric tests, two preliminary checks are crucial: Normality and Homogeneity of Variance.

📸 Video summarized with SummaryTube.com on Nov 26, 2025, 05:47 UTC