Hypothesis Testing

In statistics, hypothesis testing is a fundamental concept used to determine whether an observed effect or difference between groups is statistically significant or merely due to chance. Several statistical tests are available for this purpose, and each test is designed for specific research questions and data types. In this blog, we will discuss five popular hypothesis testing methods: one-sample t-test, two-sample t-test, paired t-test, chi-square test, and ANOVA (analysis of variance).

One-sample t-test:

A one-sample t-test is used to determine whether the mean of a sample is significantly different from a known or hypothesized population mean. The test assumes that the data are normally distributed, and the sample size is sufficient to meet the requirements of the central limit theorem. The null hypothesis states that the mean of the sample is equal to the hypothesized population mean, and the alternative hypothesis states that the mean is significantly different from the population mean.

Two-sample t-test:

A two-sample t-test is used to compare the means of two independent samples to determine whether they are significantly different. The test assumes that both samples are normally distributed, have equal variances, and the data are independent of each other. The null hypothesis states that the means of the two samples are equal, and the alternative hypothesis states that the means are significantly different.

Paired t-test:

The paired t-test is a statistical test used to compare the means of two related groups. It is a parametric test that assumes that the data is normally distributed. This test is used when we want to compare the means of the same group under two different conditions. For example, a researcher may want to investigate whether a new drug treatment leads to a significant decrease in blood pressure in patients. To test this, the researcher would measure the blood pressure of each patient before and after the drug treatment and use the paired t-test to compare the means of the two groups.

The paired t-test involves calculating the difference between the two groups' means and dividing the result by the standard deviation of the differences. The resulting t-value is then compared to a critical value based on the degrees of freedom and the desired level of significance. If the calculated t-value is greater than the critical value, we can conclude that the two means are significantly different.

Chi-square test:

The chi-square test is a statistical test used to determine whether there is a significant association between two categorical variables. This test is used to analyze data in the form of counts or frequencies. The chi-square test is a non-parametric test, which means it does not assume that the data follow a specific distribution.

The chi-square test involves calculating the expected frequency of each cell based on the null hypothesis, which assumes that there is no association between the two variables. The observed frequency is then compared to the expected frequency, and the resulting chi-square value is compared to a critical value based on the degrees of freedom and the desired level of significance. If the calculated chi-square value is greater than the critical value, we can conclude that there is a significant association between the two variables.

ANOVA:

It is a statistical method used to analyze the differences between two or more groups. It is a parametric test that examines whether there are any significant differences between the means of two or more groups by comparing the variation within each group to the variation between the groups. ANOVA is commonly used in experimental research to determine whether there are any significant differences between groups, such as in a clinical trial comparing the effectiveness of two different treatments. ANOVA produces an F-statistic, which is used to test the null hypothesis that there is no difference between the groups. If the F-statistic is significant, it means that there is a significant difference between the groups, and further post hoc tests may be conducted to determine which groups are significantly different from each other. ANOVA assumes that the data are normally distributed and that the variances are equal between the groups. If these assumptions are not met, non-parametric tests may be used instead.

These were some main tests which you need to know in order to start with machine learning and eda. Subscribe to the newsletter for more such articles.

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