When the assumptions about population distribution are met, the statistical methods, known as parametric tests, are applied. Generally, these tests make such assumptions as data should take normal distribution, and populations that the samples are drawn should have equal variance. When used properly, they come with good and powerful results, and they are widely used by researchers and data analysts. A number of parametric tests have different results, e.g. for the assessment of relationship or equality of variances or comparison of means. So, one has to familiarize oneself with these tests and their uses.

T-Test

It is a widely used types of parametric test to compare the means of two groups to see whether there is a significant difference between two groups. First, it makes the assumption that the data is normally distributed and second, it assumes that variances are equal. We have three main types: the independent samples t-test, the paired samples t-test and one sample t-test. In the independent samples t test, the two groups are unrelated to each other while in paired samples t test, the same group is examined at different times. In one sample t test is used to check whether the sample mean significantly differs from an already known population mean.

Analysis of Variance (ANOVA)

ANOVA (Analysis of Variance) is a comparison of the means of different groups to determine if the means are different statistically. The t test is extended for the analysis of multiple groups and thus reduces the risk for Type I errors. One of the most commonly used ANOVA methods is a one way ANOVA (also referred to as simply one way ANOVA) which compares groups on one or more factors, whereas a two way ANOVA (also called a two way ANOVA) examines the impact of two apart from variables. Tukey’s test may be conducted if significant differences are found.

Pearson Correlation Coefficient

The Pearson correlation coefficient is a measure of strength and direction of relationship between two continuous variables. It also assumes that both the variables are distributed normally and they have a relationship in a linear way. It lies within the range of -1 to 1 where -1 indicates a strong negative correlation, 0 stands for no correlation; whereas 1 means a strong positive correlation. They use this test quite widely in the field of psychology, economics, and social sciences testing associations between different variables and prediction of trends using a given dataset.

Regression Analysis

Regresi analysis is a statistical method where we can find out how one dependent variable is linked to one or more dependent variables. First of all, it takes residuals to be normally distributed and homoscedastic according to the help page. The most common type of regression is linear, where we consider linear relationships between variables. The extension of this approach to multiple independent variables is in the multiple regression in which one can use multiple independent variables to predict the dependent variable. Regression models are widely applied in forecasting trends, understanding the influence that a particular outcome is affected by, and making data driven decisions in the financial, marketing and healthcare to name a few.

Chi-Square Test for Goodness of Fit

To check if observed frequencies are significantly different from expected frequencies, a chi-square test for goodness of fit is used. The use of this test is particularly beneficial with categorical data. It makes an assumption that the sample data follows an expected probability distribution. The null hypothesis is rejected if the calculated chi-square value is larger than the critical value since there is a significant difference between observed and expected data. It is usually used in quality control, survey analysis, and market research type evaluations of distributions.

Chi-Square Test for Independence

Here we assess whether two categorical variables are related or independent using the chi square test for independence. It is a contingency table that analyzes observed frequencies as compared to expected frequencies assuming independence of variables. The test helps to determine associations between variables, that is, explain to you the relationship between customer preferences and demographic factors. This is a very significant result, which means that there is a dependency between the two variables. Usually this test is used in social sciences, epidemiology and business analytics to search patterns in data.

Mann-Whitney U Test

Still, sometimes the Mann-Whitney U test is listed in the parametric tests because it can be very useful in some cases. It tests whether there is a significant difference between the values of two independent groups when the normality assumption is not under strict conditions. The data are ranked, then the sum of ranks are compared between the groups. In particular it is widely used in medical and behavioral research when dealing with skewed distributions or very small sample sizes.

Conclusion

Parametric tests are one of the important parts of statistical analysis in which the researcher can derive meaningful results based on the numerical data. You have the flexibility to decide upon the various parametric tests commonly being t tests, ANOVA, correlation, regression, and chi square tests based on data peculiarity as well as research purposes. Assumptions associated with each test must be met to get proper results. These tests are shown to be very useful in data driven decision making by the application over different fields.