Statistics discussion response 3

Statistics discussion response 3

Please respond to these discussions with reference

Discussion 1

A z-test is a statistical analysis considering the difference between the mean of the variable a sample set and the mean of the variable in a larger population, meaning how far the sample set value deviates (distance) from the mean. Approximation is acceptable if the population size is greater than or at 30, considered a normal distribution. The sample standard deviation is a good approximation of finding the z-score with the calculations.

“A t-test is a hypothesis test in which the test statistic follows a t distribution under the null hypothesis. There are several different test statistics that fall into the category of a t-test.” (Triola, 2009) If the sample size is less than 30, the expression will not be normally distributed. T-table will be used to calculate the t-distribution when the sample size is less than 30.

Many might say the reason or performance is that the z-test is solely a function of the distribution of the sample distance while the t-test is a function of the sample (both distance and variance) from the same distribution. “Tests of the null hypothesis for comparisons involving sample means use the t-test when the conditions of the z-test cannot be met.” (Blouin, 2014). The two have led to different conclusions based on their rationale. A good rule of thumb of when a z-test would be appropriate over a t-test is by looking at the sample values: with 30 or greater value set, the z-test will give a better approximation, otherwise when the value set is less than 30, the t-test should be used.

References:

Blouin, D. C., & Riopelle, A. J. (2004). The Difference Between t and z and the Difference It Makes. Journal Of General Psychology, 131(1), 77-84. doi:10.3200/GENP.131.1.77-84

Triola (2009). Introduction to T-test. Retrieved from http://lc.gcumedia.com/hlt362v/the-visual-learner/…

Discussion 2

Sometimes, measuring every single piece of item is just not practical. That is why we developed and use statistical methods to solve problems. The most practical way to do it is to measure just a sample of the population. Some methods test hypotheses by comparison. The two of the more known statistical hypothesis test are the T-test and the Z-test.

Both z-test and t-test are necessary measures of hypothesis testing. A t-test is preferred in cases where the sample size under consideration is less than 30 and does not have a known standard deviation. On the other hand, a z-test would be preferred if the sample size is over 30 and it is necessary to determine the standard deviation of the population.

The differences in application can thus be simplified in different ways. For instance, Z-test is a statistical hypothesis test that follows a normal distribution while T-test follows a Student’s T-distribution. A T-test is appropriate when you are handling small samples (n < 30) while a Z-test is appropriate when you are handling moderate to large samples (n > 30). T-test is more adaptable than Z-test since Z-test will often require certain conditions to be reliable. Additionally, T-test has many methods that will suit any need. T-tests are more commonly used than Z-tests. Z-tests are preferred than T-tests when standard deviations are known.

References

Ian (2010). Difference Between Z-test and T-test. Retrieved from http://www.differencebetween.net/miscellaneous/dif…

Discussion 3

The T-test and the Z-test are the two of the most known statistical hypothesis. When choosing to use either the Z test or the T test there are some slight differences between the two. They are both used in hypothesis testing. The T test is used when the sample size is less then 30 and when the population standard deviation is unknown. If the same size is greater than 30 or you know the standard deviation of the population Z scores use individual scores and convert them into a standard form, then you would choose to use the Z test (Andale,2013). It is very easy and straightforward to use which could make it the most likely to be used in statistical data analysis. It is also flexible and can adapt to any circumstance. The T-test is usually applied in a theory if there is a limited sample (n < 30) and the variables are approximately normally distributed and are not very different. It can also be used when the standard deviation of the population is unknown. On the other hand, if the standard deviation of the population is known, Z-test is better used. The Z-test helps to determine if there is a difference between the sample and the population. Z-test are also applied in larger samples (n > 30). The Z-test follows a normal distribution while T-test follows student’s T- distribution. The way to find the Z score would be z=(X-μ)/σ and the way to find the T score is T= t = (x – μx) / [s/√(n) ].

Reference.

Andale. (2013, August 23). T-score verus Z-score: What’s the difference? Retrieved May 14, 2018, from Statistics How to website:

http://www.statisticshowto.com/when-to-use-a-t-sco…

Robert A. Donnelly Jr. Ph.D: The Complete Idiot’s Guide to Statistics, 2nd Edition

Discussion 4

One of the questions of the week is when a z-test would be appropriate over a t-test. To answer this question first I need to explain what both tests are.

A t-test is a hypothesis statistical test to figure out if a hypothesis is true or not. The t-test should be applied if you have a small sample size one less than 30 and there is a normal distribution. This test is also useful when the standard deviation is not known

A z-test is different in order to use a Z-test you have normal distribution of a sample size, the standard deviation should be known, and your sample size should be larger than 30. The major difference between using the two tests would be the z test uses a larger sample size and you should know the standard deviation (Ian, 2010).

I am better able to make sense of things if I can put them into an example for myself. So here is the example that I thought of to help clear it up for me. So, an example of a t-test would be if I wanted to know how my grade in this class was different than others. I am going to use the t-test because I do not know the standard deviation and there are only 17 students in the class. A z-test would be used in something like an entrance exam for a college. If I wanted to see how I did in relation to others. There would be more than 30 people and I could get the standard deviation from the college (Ian, 2010).

So, a z-test would be appropriate to use when I had a larger sample size and knew the standard deviation.

Reference

I. (2010, January 05). Difference Between Z-test and T-test. Retrieved May 15, 2018, from http://www.differencebetween.net/miscellaneous/dif…

Discussion 5

The t-test is easy to calculate and used to determine differences between two groups. A t-test is a hypothesis test used for comparing data, that has been placed in two categories. It analyzes the average of the two categories. A t-test is used to compare simple random data of sizes that are less than 30 but greater than 5. A t-test should be used when the standard deviation is unknown. The t-test graph would have more on the tails and a shorter center. This test is easy to calculate and used to determine differences between two groups.

A z-test is used to compare two sample sizes of data greater than 30. The z-test is used when the standard deviation is known. A z-test assumes a normal shape of the graph with even distribution. A z-test would be appropriate to use in cases where determining if keeping a room darkened in a new born intensive care had a direct correlation to the infants requiring less oxygen. In this study there would have to be infants on ventilators or requiring supplemental oxygen to keep their saturations greater than ninety-two. The test would include a sample size of forty infants, male and female of the medical background.

S, S. (2018, March 20). Difference Between t-test and z-test (with Comparison Chart). Retrieved May 15, 2018, from https://keydifferences.com/difference-between-t-te…

Discussion 6

A z-score is a measure of standard deviation that helps the researcher to know whether to accept or reject the null hypothesis. The null hypothesis is basically a hypothesis that says there is no statistical meaning to a set of data and that there is not relationship between the variables (Investopedia, 2018). If a sample size is greater than thirty, then the data is normally distributed and the sample standard deviation is a good indicator of the entire population’s standard deviation and because of this, a z-statistic should be used (Khan Acadamy, n.d.). A z-score is also used when the standard deviation is not known (Khan Acadamy, n.d.).

When a t-score is used, it involves comparing the means for two different groups in the study while adjusting for any variability that may be present in the samples. The larger the t ratio is, the more variability there is between the groups. A t-test should be used when the sample size is less than thirty because it will not be normally distributed (Khan Acadamy, n.d.). T-tests can be used for dependent or independent samples in a study (Grover & Cipher, 2017). Independent samples would when one group in the sample is different and does not have similarities to other samples in another group. A dependent sample is one that is assessed repeatedly (Grove & Cipher, 2017).

Staff, Investopedia (2018, March 15). Null Hypothesis. Retrieved from https://www.investopedia.com/terms/n/null_hypothes…

Khan Academy. (n.d.). Z-statistics vs. T-statistics. Retrieved from https://www.khanacademy.org/math/statistics-probab…

Grove, S. K., & Cipher, D. J. (2017). Statistics for Nursing Research: A Workbook for Evidence Based Practice. St. Louis, MO: Elsevier.