Wk 6 Discussion 1 - Confidence Intervals [due Thurs]

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Wk 6 Discussion 1 - Confidence Intervals [due Thurs] Due Thursday When implementing a research study, it is important to know the relationship between confidence intervals, sample sizes, and estimated standard errors. Write a 250- to 300-word response to the following: Explain the relationship between confidence intervals, sample sizes, and estimated standard errors. How might understanding these elements be useful in understanding your mock data used throughout this course? Confidence intervals (CI) is the best estimate for the range of a population value that researchers come up with given the sample value. The confidence interval gets larger as the probability of being correct increases. A standard error of the mean gives a range (the confidence interval) of there the mean and the entire population likely lies. A standard error is the standard deviation of the sampling distribution. Standard errors are related to confidence intervals. A sample size ensures the validity and reliability of a research study (Frankfort-Nachmias et al., 2019). As a sample size increases the standard error decreases because with a larger sample size, there is less variation between sample statistics. It is important for a researcher to understand these elements in order to better understand the data collected, likewise, making it important for doctoral students to understand the data collected for mock trials during this course. In looking at the data, if the sample size increases, the standard error falls and the chance of variation is reduced. By decreasing error possibilities, this increases the validity and reliability of a researcher’s study. Confidence intervals ensure the researcher how sure they can be about their data and findings and the standard error is used to estimate the efficiency and accuracy of a sample. The standard error is the most useful as a means of determining the confident level. Therefore, all three concepts are interrelated and equally important to a researcher (Altman, 2005). Altman, D. G. (2005). Standard deviations and standard errors. The BMJ , 331. https://doi.org/10.1136/bmj.331.7521.903
Frankfort-Nachmias, C., Leon-Guerrero, A., & Davis, G. (2019). Social statistics for a diverse society (9th ed.). SAGE Publications. The standard error falls as the sample size increases, as the extent of chance variation is reduced—this idea underlies the sample size calculation for a controlled trial, A confidence interval (or CI) is the best estimate of the range of a population value (or population parameter) that we can come up with given the sample value (or sample statistic). the larger range of the confidence interval allows you to encompass a larger number of possible outcomes and you can thereby be more confident. The confidence interval gets larger as the probability of being correct increases. . the standard error of the mean is the standard deviation of all the possible means selected from the population. It’s the best estimate of a population mean that we can come up with, given that it is impossible to compute all the possible means. If our sample selection were perfect, and the sample fairly represents the population, the difference between the sample and the population averages would be zero, right? Right. If the sampling from a population were not done correctly (randomly and representatively), however, then the standard deviation of all the means of all these samples could be huge, right? Right. So we try to select the perfect sample, but no matter how diligent we are in our efforts, there’s always some error. The standard error of the mean gives a range (remember that confidence interval from Chapter 9?) of where the mean for the entire population probably lies. There can be (and are) standard errors for other measures as well. Earlier in this lesson we learned that the sampling distribution is impacted by sample size. As the sample size increases the standard error decreases. With a larger sample size there is less variation between sample statistics , or in this case bootstrap statistics. Let's look at how this impacts a confidence interval. The   standard deviation   is a measure of the variation or dispersion of data, how spread out the values are. The   standard error   is the standard deviation of the sampling distribution.  Standard errors are related to confidence intervals. A   confidence interval   specifies a range of plausible values for a statistic. A confidence interval has an associated   confidence level . Ideally, we want both small ranges and higher confidence levels.
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