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###### Yisehak Beyene
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# Inferential data analysis techniques

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Inferential data analysis techniques are used to draw conclusions and make predictions about a population based on a sample of data. Some common inferential data analysis techniques include:

1. Hypothesis testing: This technique involves testing a hypothesis about a population parameter using sample data. The goal is to determine whether the observed difference between the sample data and the hypothesized value is statistically significant.

2. Confidence intervals: Confidence intervals provide a range of values within which the true population parameter is likely to fall. This technique helps to quantify the uncertainty associated with estimating population parameters from sample data.

3. Regression analysis: Regression analysis is used to examine the relationship between one or more independent variables and a dependent variable. It helps to predict the value of the dependent variable based on the values of the independent variables.

4. Analysis of variance (ANOVA): ANOVA is used to compare the means of two or more groups to determine if there is a statistically significant difference between them. It is often used in experimental research to test the effectiveness of different treatments or interventions.

5. Chi-square test: The chi-square test is used to determine whether there is a significant association between two categorical variables. It is commonly used in survey research and social science studies.

These are just a few examples of inferential data analysis techniques that are commonly used in research and data analysis. By using these techniques, researchers can make informed decisions and draw meaningful conclusions from their data.
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Statistical Hypothesis Testing

- Null hypothesis significance testing (NHST): Tests whether there is sufficient evidence to reject the null hypothesis that there is no difference between groups or relationships between variables.
- Confidence intervals: Estimates the range within which a population parameter, such as a mean or proportion, lies with a specified level of confidence.
- p-values: Determine the statistical significance of a difference or relationship by representing the probability of observing the sample results if the null hypothesis were true.

Regression Analysis

- Simple linear regression: Models the relationship between a single predictor variable and a response variable, estimating the slope of the line and the intercept.
- Multiple linear regression: Extends simple linear regression to include multiple predictor variables.
- Logistic regression: Models the probability of a categorical outcome (e.g., success or failure) as a function of independent variables.

Analysis of Variance (ANOVA)

- One-way ANOVA: Tests whether the means of three or more independent groups are different.
- Two-way ANOVA: Tests whether the means of two or more independent groups differ across two or more conditions.
- Repeated measures ANOVA: Tests whether the means of a dependent variable differ across multiple measurements taken from the same subjects or groups.

Non-Parametric Tests

- Chi-square test: Tests for the independence of two categorical variables.
- Mann-Whitney U test: Tests for differences between two independent groups when the data is non-normally distributed.
- Kruskal-Wallis test: Tests for differences between three or more independent groups when the data is non-normally distributed.

Bayesian Analysis

- Bayesian inference: Uses Bayes' theorem to update beliefs about unknown parameters based on observed data, incorporating prior knowledge and calculating posterior probabilities.
- Credible intervals: Represent the range within which a parameter is likely to fall based on the posterior probability distribution.

Machine Learning

- Supervised learning: Classifies data based on labeled training data.
- Unsupervised learning: Identifies patterns and structures in unlabeled data.

Time Series Analysis

- Exponential smoothing: Forecasts future values based on past values.
- Autoregressive integrated moving average (ARIMA) models: Capture patterns and trends in time series data.
- Cross-correlation: Identifies relationships between multiple time series.
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