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An important part of using statistics is being able to explain your results to decision makers. Imagine that you have conducted a two-sample test and determined that the difference was not statistically significant. While one mean was 4.3 and the other was 3.9, the p level for the t test was p=.07. Your management team says, â€œWell, the difference may not be statistically significant, but the difference is there! Discuss how you would respond and how you would explain the purpose of the t test and significance in this case.
REPLY TO THE FOLLOWING;
Hello, In response to Week 5 Discussion
The meaning of the phrase â€œstatistically significantâ€ in statistics, means that the result of the analysis or experiment is unlikely due to chance, and a decision has been made to reject the null hypothesis, meaning something is different.
So, if we say something is not statistically significant, we are saying that the result may be likely due to chance. We accept the null hypothesis, that declares that there is no difference between what we expect and what was determined in the analysis-
In business, the word significant is sometimes likely to imply â€œimportantâ€, or a large amount or degreeâ€. So, just because a result is not statistically significant, does not mean that it is not a significant business result.
The phrase â€œSubstantive resultâ€ is when the result or outcome of a statistical study produces results that are important to the decision makers. The result in this case are Substantive, but not significant, by statistician terms. We need to be aware of the differences between the statistically significant and Substantive results.
In this case we used a t-test in the statistical study, which means we did not know the population standard deviation, so we had to use the sample standard deviation as an estimate of it. We assume the population is normally distributed. If the alpha = .05 for a 95 percent confidence, and the p-value is determined to be .07, since the p-value is greater than the alpha, we say that there is not enough evidence found in the sample to reject the null hypothesis, so this supports us saying that there is no difference and the result is not statistically significant.
As illustrated in chapter 10, the approach as to whether to use a z statistic or a t statistic for analyzing the differences in two sample means is the same as that used in chapters 8 and 9. When the population variances are known, the z statistic can be used. However, if the population variances are unknown and sample variances are being used, then the t test is the appropriate statistic for the analysis. It is always an assumption underlying the use of the t statistic that the populations are normally distributed. If sample sizes are small and the population variances are known, the z statistic can be used if the populations are normally distributed.
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