Explain the central theorem limit.

Explain the central theorem limit.

Explain the central theorem limit. 150 150 Nyagu

PUB-550 Topic 2: Probability and Confidence Intervals discussion questions
PUB-550 Topic 2: Probability and Confidence Intervals discussion questions

Topic 2: Probability and Confidence Intervals
Objectives:
Apply descriptive statistics to describe qualitative and quantitative characteristics of a sample.
Demonstrate how probability and normal distribution are used to determine significance.
Apply a sample standard deviation to describe a variable and its dispersion.
Explain the central theorem limit.
Evaluate the application of confidence intervals in public health research.
PUB-550 Topic 2: Probability and Confidence Intervals discussion questions
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Topic 2 DQ 1
P-values and confidence intervals are both used in hypothesis testing. Explain three reasons why it may be preferable to report a confidence interval over a P-value. Provide a specific example to justify your reasons.

Topic 2 DQ 1

The use of P-values and Confidence Intervals (CIs) are important for understanding evaluations of scientific studies. Specifically, they are used in evaluating hypothesis testing. A P value is the core of statistical inference method but is limited to dichotomous evaluation whether null is statistically significant or not (Lee, 2016). An alternative approach that is more informative that P value is confidence intervals. Whereas with P values an investigator could state P0.05, there is little information about the direction or size of the differences (Gardner & Altman, 1986). CIs gives a greater amount of information of the magnitude and precision of the measurement.

The first reason that confidence intervals may be preferable over P-values is that confidence intervals are interval estimates for population value rather than a single point value. Researchers are able to take a sample from a larger population, calculate the sample mean, and construct a range (Confidence interval), that has a greater probability of containing the population mean than a point estimate (Corty, 2016).

The second reason confidence intervals may be preferable over P-values, is that they are not limited to dichotomous significant or not significant, but rather are able to provide the magnitude of the effect. A 95% confidence interval means that the population mean is within the range of 95% of confidence interval of the calculated mean with a probability of 95% (Lee, 2016). With the increase of sample size, the confidence interval narrows while limits of significance remain unchanged. For example, statistical results that may have the same P-value, the estimated confidence interval narrows with a larger sample size indicating a more reliable result (Lee, 2016). PUB-550 Topic 2: Probability and Confidence Intervals discussion questions.

The third reason confidence intervals may be preferable over P-values, is that p values enable recognition of statistically noteworthy findings, whereas confidence intervals provide information about the range in which the true value of the population lies within a certain degree of probability, as well as direction and strength of the effect (du Prel, Hommel, Rohrig, &Blettner, 2009) PUB-550 Topic 2: Probability and Confidence Intervals discussion questions. The smaller the P-value the more statistically significant and stronger the evidence is. Confidence intervals reflect results at the level of data measurement, and include the desired parameter within a certain probability (du Prel et al., 2009).

References

Corty, E. Using and interpreting statistics: A practical text for behavioral, social, and health sciences (3rd ed.). New York, NY: Macmillan Learning.

du Prel, J-B., Hommel, G., Rohrig, B., & Blettner, M. (2009). Confidence interval or P-value. Deutschees Arzteblatt International, 106(19), 335-339. doi: 10.3238/arztebl.2009.0335 PUB-550 Topic 2: Probability and Confidence Intervals discussion questions

Gardner, M. J. & Altman, D. G. (1986). Confidence intervals rather than P values: estimation rather than hypothesis testing. British Medical Journal, 292, 746-750. Retrieved from https://www.bmj.com/content/bmj/292/6522/746.full.pdf

Lee, D. K. (2016). Alternatives to P value: confidence interval and effect size. Korean Journal of Anesthesiology, 69(6), 555-562. doi: 10.4097/kjae.2016.69.6.555

Topic 2 DQ 2

During the simulation the results of increasing the sample size really didn’t change the curve at all. The central limit theorem demonstrates how much sampling error exists in samples by taking repeated random samples from a population, calculating the mean for each sample and then making a frequency distribution of the mean (Corty, 2016). The theory predicts that the standard error of the mean can be calculated if one knows the population standard deviation and the size of the sample (Corty, 2016). The theory also predicts that the sampling distribution is normally distributed, and the mean of the sampling distribution is the mean of the population (Corty, 2016).

I found this example from an unofficial source, but I found it descriptive – Find an old stone step or lintel in front of a doorway (one that is old enough that it has been worn down by generations of people walking over it). If you look at how it is worn down, the wearing down won’t be uniform over the surface of the step: rather, it will be in a bell-curve. (People tend to walk through the middle of the doorway.) If the door doesn’t open all the way, the bell-curve won’t be perfect; there will a bias towards the side away from the hinges”. For some reason this helped cement the theory for me, the bell curve is “where most of the samples walk through the doorway”. PUB-550 Topic 2: Probability and Confidence Intervals discussion questions

References

Cool Examples of Central Limit Theorem in Action. Retrieved from https://math.stackexchange.com/questions/38825/cool-examples-of-the-central-limit-theorem-in-action.

Corty, E. W. (2016). Using and Interpreting Statistics. New York: Worth Publishers . PUB-550 Topic 2: Probability and Confidence Intervals discussion questions