18 Nov What do you consider to be the difference between independent t-test and dependent t-test?

What do you consider to be the difference between independent t-test and dependent t-test?

The dependent t test, (the paired samples t test) compares the means between two related groups on the same continuous dependent variable.

The independent t-test, (Student’s t-test), is a test within inferential statistics used to determine the statistical significance difference between the means of two nonrelated groups. The null and alternative hypotheses for the independent t-test.

What non-parametric statistical analysis can you use if the data do not meet the assumptions of parametric analysis?

In statistics, the chi-square test is the main non-parametric method, however, exists other tests, that are comparable to the parametric tests and are applied when the data have not the expectations for the parametric studies.

Some examples are:

Chi-square test: this test establishes if there is an association between two categorical variables.

Kruskal-Wallis test: a non-parametric alternative to the one-way ANOVA, to find out if the median of two or more groups is different. 

Friedman test: non-parametric choice to one-way ANOVA with repeated measures, to test for differences between groups when the dependent variable being measured is ordinal.

Other examples are Mann-Whitney U test, One-Sample Sign Test; Mood’s median Test; Mann-Kendall Trend test. 

When do you use ANOVA? 

ANOVA (analysis of variance) is a statistical test that makes a single, general decision about whether there is a significant difference between three or more sample means. An ANOVA is like a t-test. However, ANOVA can also test multiple groups to see if they differ on one or more variables.

ANOVA is used to compare the variances between the means (or the mean) of different groups. It is used by a variety of contexts to determine if there is any difference between the means of the different groups.

One-way ANOVA: is used for three or more data sets to determine the relationship between the dependent and independent variables.

A two-way ANOVA: is used to estimate how the mean of a quantitative variable changes according to the levels of two categorical variables. We use Two-way ANOVA when we want to know how two independent variables, in combination, can affect a dependent variable.

If you cannot identify where the differences occur in groups, what statistical procedure can you apply? 

When the independent variable has a scale of interval, it is necessary to know the probability of the distribution of the population. If the data have a similar probability of distribution to normal (Gaussian), we should use parametric tests to evaluate the proposed hypotheses. Otherwise, we should use non-parametric methods that can also be applied to ordinal variables. 

In cases with reduced sample size, in which the distribution probability of the response variable is unknown, and there is no further evidence, we will use nonparametric tests.  In some cases, the choice enters one and another test will be based solely on the larger of the sample as this is the case of the Fisher’s exact test that is used as an alternative to the chi-square test, when there is not enough sample for meeting the demands of the latest test.

References

Mishra, P., Singh, U., Pandey, C., Mishra, P., & Pandey, G. (2019). Application of student’s t-test, analysis of variance, and covariance. Annals of Cardiac Anaesthesia, 22(4), 407. https://doi.org/10.4103/aca.aca_94_19