# Essays on Statistics Article

Figure 424List of TablesTable 1: Independent Samples Test6Table 2: Descriptives10Table 3: Test of Homogeneity of Variances10Table 4: ANOVA11Table 5: Ranks12Table 6: Test Statisticsa12 Table 7: Ranks14Table 8: Test Statisticsa, b15Table 9: preexisting hypertension * alive discharge Crosstabulation17Table 10: Chi-Square Tests18Table 11: Directional Measures18Table 12: Symmetric Measures19Table 13: Coefficientsa25Table 14: ANOVAb26Table 15: Model Summaryb26[Writer’s Name][Instructor’s Name][Course][Date]Hypothesis TestingIndependent Samples t-test Assumptions Assumptions of the Independent Sample t Test: The variances of the dependent variable in the two populations are equal. The dependent variable is normally distributed within each population. The data are independent (scores of one participant are not related systematically to scores of the others).

Evaluation of the AssumptionsSPSS automatically test assumption 1 with the Levene test for equal variances. Assumption 2 could be tested with the Explore command, to see that the dependent variables are at least approximately normally distributed for each gender. However, the t test is quite robust to violations of this assumption; therefore this assumption needs not to be tested. Assumption 3 probably is met because the genders are not matched or related pairs and there is no reason to believe that one person’s score might have influenced another person’s.

Hypothesis StatementH0: There is no difference in the mean length of stay in hospital for males vs. females. H1: There is a difference in the mean length of stay in hospital for males vs. females. AnalysisThe procedure produces two tests of the difference between the two groups. One test assumes that the variances of the two groups are equal. The Levene statistic tests this assumption. In this example, the significance value of the statistic is 0.505 (See Sig. under Levene's Test for Equality of Variances).

Because this value is greater than 0.05, we can assume that the groups have equal variances and ignore the second test. The t column in Table 1 presents the observed t statistic for each sample, calculated as the ratio of the difference between sample means divided by the standard error of the difference. The column labeled Sig. (2-tailed) displays a probability from the t distribution with 82 degrees of freedom. The value listed is the probability of obtaining an absolute value greater than or equal to the observed t statistic, if the difference between the sample means is purely random.

The 95% Confidence Interval of the Difference provides an estimate of the boundaries between which the true mean difference lies in 95% of all possible random samples of 84 students. Table 1: Independent Samples TestLevene's Test for Equality of Variancest-test for Equality of MeansFSig. tdfSig. (2-tailed)Mean DifferenceStd. Error Difference95% Confidence Interval of the DifferenceLowerlength of stay in hospitalEqual variances assumed. 448.505.33982.736.8812.599-4.2906.052Equal variances not assumed. 36562.067.716.8812.411-3.9395.701Conclusion and DiscussionSince the significance value of the t- test is greater than 0.05 (P = 0.736 > 0.05, Table 2), we fail to reject the null hypothesis.

That is there is no difference between male and female in regard to their length of stay in hospital. The independent-samples t test is appropriate whenever two means drawn from independent samples are to be compared. As with all t tests, the independent-samples t test assumes that each sample mean comes from a population that is reasonably normally distributed, especially with respect to Skewness. Test variables with extreme or outlying values should be carefully checked; or non-parametric test can be used to be sure.