There are several assumptions for the use of an independent samples t test. State each of these and the implications should these assumptions be violated. Is it possible for a p value to equal 0? Why or why not? 

Warner (2019) highlights a number of assumptions while using the independent sample t test. These assumptions and they include;

1. Assumption of independence-Independence both within and between groups- This assumption implies that when looking at the scores between groups it is expected that each score belongs to only one group. A subject in one group cannot be in another group. If this assumption is violated, such that the scores are pairing, matching or repeated, then an independent sample t-test cannot be carried out and the researcher should consider using the paired ample t test (Warner, 2019). As an example, a researcher wants to determine if the test scores of females and males are different and whether these differences could have occurred because of chance. In this case, the assumption of independence between groups is that all the scores in this example will only belong to only two groups either male or female. On the other hand, the assumption further states that the Y scores should also be independent of each other when compared within the group. This means that each score has no influence on the other. In a research scenario, Warner (2019) states that this can be avoided in the data collection phase by collecting data individually among participants. However, if data is not collected individually, then there is little that can be done once data has been collected and because it is also difficult to screen and detected the non-dependence within groups (Warner , 2019).Warner, (2019) state that ,if this assumption is violated, then the independent sample t tests cannot be used.
2. Assumption of normality -This assumption is that the score of the dependent variable are distributed normally within each of the two populations as defined by the grouping variable (Warner, 2019).A researcher can use the Shapiro- Wilks tests to determine whether to retain the null hypothesis that the assumption of normality has been met or to reject the null hypothesis in favor of the alternative hypothesis that indicate the assumption of normality has not been met .If the assumption of normality are not met two alternative that a research can use is to transform the data to become normally distributed or run non parametric test which do not require that this assumption be met(Lund Research , n.d.).The implication of running and independent t test on data that is not normally distributed is that it weakens the tests (Kent State University , n.d.).However, Warner(2019) state that if  this assumption is violated, such that the data lack normality but has equal variance, then there  are no serious implications unless the sample used is very small and outliers exist within the groups .
3. Assumption of homogeneity of variance -This assumption states that the variances of the groups that are being measured are equal in the population, A violation of this assumption, results in type I error rate. A researcher can avoid making this error by carrying out a Levene’s F test for equality of variances when running the independent sample T test(Warner, 2019). The test provides an F statistic and a significance value which is the p value. If the p value shows significance, that is p < 0.05, then the assumption has been violated. A research can correct this violation using the Welch-Satterthwaite method that adjust the degrees of freedom (NAU.edu, n.d.).
4. The Y scores are usually quantitative -This is because we are calculating a group mean and therefore means are quantitative in nature and would never be categorical. If the Y variable is categorical as opposed to ratio, then the test cannot be carried out and neither would it make sense (Warner,2019).
5. Assumption that no outliers within groups-Even though this is not stated as a formal assumption, Warner (2019) state that the presence of outliers affects data analysis in the independent sample t test. This comes from the fact that we are comparing means which are not robust against outliers because normality of data is affected especially in cases where the outliers are extreme. The implication of violating this assumption is that the p value obtained on a data set that has extreme outliers will have P value outcomes that are either under or overestimated risk f type one error (Warner, 2019).

Is it possible for a p value to equal 0? Why or why not? 

From the understanding of P value, it can never be zero. It lies along a continuum of 0 and 1.P value describes probability and therefore we can never be certain about a given outcome especially in hypothesis testing we can only be confident about an outcome. Therefore, P value is a regarded as a continuous variable along a probability continuum that lies between 0 and 1 (Andrade, 2019).