Common Statistical Tests and Techniques Mentioned in the Syllabus

Hypothesis Testing:
- Hypothesis testing is a statistical technique used to make inferences or draw conclusions about a population based on sample data.
- It involves setting up a null hypothesis (H0) and an alternative hypothesis (Ha) and testing the evidence against the null hypothesis.
- Commonly used tests for hypothesis testing include t-tests, chi-square tests, ANOVA, and regression analysis.

T-tests:
- T-tests are used to compare the means of two groups and determine if there is a significant difference between them.
- There are three types of t-tests: independent samples t-test, paired samples t-test, and one-sample t-test.

Chi-square Test:
- The chi-square test is used to determine if there is a significant association between two categorical variables.
- It compares the observed frequencies with the expected frequencies under the assumption of independence.

Analysis of Variance (ANOVA):
- ANOVA is used to compare means across three or more groups to determine if there is a significant difference between them.
- It tests the null hypothesis that the means of all groups are equal.

Regression Analysis:
- Regression analysis is used to model the relationship between a dependent variable and one or more independent variables.
- It helps in predicting the value of the dependent variable based on the values of the independent variables.

Correlation Analysis:
- Correlation analysis measures the strength and direction of the linear relationship between two continuous variables.
- It is expressed by the correlation coefficient, which ranges from -1 to +1.

Time Series Analysis:
- Time series analysis involves analyzing and forecasting data collected over time.
- It includes techniques like moving averages, exponential smoothing, and autoregressive integrated moving average (ARIMA) models.

Factor Analysis:
- Factor analysis is used to identify underlying factors that explain the pattern of correlations among a set of observed variables.
- It helps in reducing the dimensionality of data and identifying latent variables.

Cluster Analysis:
- Cluster analysis is a technique used to group similar objects or data points into clusters based on their similarities or dissimilarities.
- It helps in identifying patterns and grouping similar data points together.

Non-parametric Tests:
- Non-parametric tests are used when the assumptions of parametric tests are violated or when the data is not normally distributed.
- Examples of non-parametric tests include Mann-Whitney U test, Kruskal-Wallis test, and Wilcoxon signed-rank test.

Sampling Techniques:
- Sampling techniques are used to select a subset of individuals or observations from a larger population.
- Common sampling techniques include simple random sampling, stratified sampling, cluster sampling, and systematic sampling.

Experimental Design:
- Experimental design involves planning and conducting experiments to study the effects of one or more variables on a dependent variable.
- It includes techniques like randomized controlled trials, factorial designs, and Latin square designs.

Statistical Software:
- Statistical software such as SPSS, R, and SAS are commonly used for data analysis and conducting statistical tests.
- These software provide a range of functions and tools for descriptive statistics, hypothesis testing, regression analysis, and more.

Overall, the syllabus covers a wide range of statistical