what is statistical inference? mention major areas of statistical inference and define each of them
From Wikipedia:
Statistical inference is the process of using data analysis to infer properties of an underlying distribution of probability. Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population.
I'll leave the rest to you.
Statistical inference refers to the process of drawing conclusions or making predictions about a population based on the information obtained from a sample. It involves utilizing statistical methodologies to make inferences or generalizations about a larger population.
There are several major areas of statistical inference, each serving a unique purpose. Let's define each of them:
1. Estimation: Estimation is focused on estimating unknown population parameters based on sample data. It involves calculating point estimates, such as the sample mean or proportion, and interval estimates, such as confidence intervals, to determine the range of values within which the population parameter is likely to fall.
2. Hypothesis Testing: Hypothesis testing involves making conclusions or decisions about a population parameter based on sample data. It starts with a null hypothesis (H0) that assumes no statistical significance or relationship, and an alternative hypothesis (H1) that contradicts or challenges the null hypothesis. Statistical tests, such as t-tests or chi-square tests, are used to determine if the evidence supports rejecting the null hypothesis in favor of the alternative hypothesis.
3. Confidence Intervals: Confidence intervals provide a range of values within which the true population parameter is likely to lie. By specifying a confidence level (e.g., 95% confidence), we can estimate the level of certainty in the interval. It is useful when estimating unknown population parameters, as it provides a measure of the precision and uncertainty of the estimate.
4. Regression Analysis: Regression analysis is used to identify and quantify the relationship between a dependent variable and one or more independent variables. It helps understand how changes in the independent variables are associated with changes in the dependent variable. The most common form is linear regression, where a linear equation is fitted to the data to predict the value of the dependent variable.
5. Analysis of Variance (ANOVA): ANOVA is employed to compare means between multiple groups or categories. It examines whether there are any significant differences in the means of different groups and calculates if these differences are statistically significant.
6. Non-parametric Methods: Non-parametric methods are used when the assumptions required by traditional parametric methods are violated. These methods rely on fewer assumptions and are suitable for data that do not follow a specific distribution. They include methods like the Wilcoxon rank-sum test, Kruskal-Wallis test, and chi-square test for independence.
These are just a few of the major areas within statistical inference. Each of them plays a crucial role in analyzing and interpreting data, helping researchers and analysts make meaningful conclusions and predictions about populations based on sample data.