See attachment..... From previous assignments
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?
Include your own experience as well as 2 citations that align with or contradict your comments as sourced from peer-reviewed academic journals, industry publications, books, and/or other sources. Cite your sources according to APA guidelines. If you found information that contradicts your experience, explain why you agree or disagree with the information.
Due Monday
Review your classmates’ initial post and provide additional information and/or insights related to the examples they offered. You should respond to at least one classmate in a minimum of 150 words.
Respond to Derrick
The relationship between confidence intervals (CIs), sample sizes, and estimated
standard errors are crucial for research study design and interpretation, as these
statistical concepts significantly impact the reliability and precision of findings.
A confidence interval is a range within which the true population parameter is
expected to fall, typically at 95% confidence. The width of this interval depends on
two factors: sample size and the standard error (SE). The standard error represents the
variability of a sample statistic, calculated by dividing the standard deviation by the
square root of the sample size. As sample size increases, the standard error decreases,
narrowing the confidence interval and providing more precise estimates (McClave &
Sincich, 2021)
Understanding the relationship between sample sizes and confidence intervals is
crucial for accurate interpretation of results. Small sample sizes initially result in
wider confidence intervals, indicating less certainty about estimates. However, as
sample sizes increase, the intervals narrow, enhancing group differences clarity. This
aligns with McNeish and Stapleton (2016)'s findings that adequate sample sizes
reduce estimation bias and ensure more accurate confidence intervals in educational
research. Standard error also helps avoid overconfidence in point estimates, as smaller
standard errors indicate the sample mean is likely close to the population mean,
improving results credibility. Kline (2019) supports this concept, stating that standard
errors quantify the precision of sample estimates and are essential in constructing c
onfidence intervals and hypothesis testing.
Greenland et al. (2016) suggest that confidence intervals (CIs) should not be
interpreted as absolute truth indicators, but as a spectrum of plausible values
influenced by assumptions. This perspective is particularly useful when dealing with
omplex, non-random samples or unknown population variances.
Understanding statistical elements like confidence intervals, sample sizes, and
standard errors were crucial for designing effective sampling strategies and interpreting
data with skepticism. It guided decisions on increasing sample size or adjusting for
variability, improving the robustness of mock analyses. Recognizing these
relationships directly impact the quality and credibility of empirical research.
References
Greenland, S., Senn, S. J., Rothman, K. J., Carlin, J. B., Poole, C., Goodman, S. N., &
Altman, D. G. (2016). Statistical tests, P values, confidence intervals, and power: a
guide to misinterpretations. European Journal of Epidemiology, 31(4), 337–350.
https://doi.org/10.1007/s10654-016-0149-3
Kline, R. B. (2019). Becoming a behavioral science researcher: A guide to producing
research that matters (2nd ed.). Guilford Press.
McClave, J. T., & Sincich, T. (2021). Statistics (14th ed.). Pearson. McNeish, D., &
Stapleton, L. M. (2016). The effect of small sample size on two-level model estimates:
A review and illustration. Educational Psychology Review, 28(2), 295–314.
https://doi.org/10.1007/s10648-014-9287-x
Due Saturday
Refer to the research question and hypotheses you created in Week 1.
Write a 250- to 300-word response to the following:
Discuss each of the 5 steps in hypothesis testing as it relates to your data.
Note: You will only need to explain steps 4 and 5 in general, but steps 1-3 should be fairly specific to your data.
Due Monday
Review your classmates’ initial post and provide additional information and/or insights related to the examples they offered. You should respond to at least one classmate in a minimum of 150 words.
Respond to Jalen
In applying the five steps of hypothesis testing to my research on how education and income levels influence social trust among U.S. adults, the process begins with Step 1, where I state my hypotheses. The null hypothesis (H₀) asserts that there is no significant relationship between education level and income level on social trust, while the alternative hypothesis (H₁) suggests that higher education and income are associated with increased social trust.
Step 2 involves setting the significance level at 0.05, which determines the threshold for deciding whether the observed results are statistically significant.
Step 3, I will analyze the data by conducting an appropriate statistical test—likely a chi-square test for independence, given the categorical nature of the variables—to examine the relationship between education, income, and trust.
In Step 4, I will compare the p-value obtained from the analysis to the alpha level. If p < 0.05, I will reject the null hypothesis, indicating a significant association between education, income, and social trust. Conversely, if p ≥ 0.05, I will fail to reject H₀, suggesting insufficient evidence to support a relationship.
Step 5 involves interpreting these results within the context of my study. If a significant relationship is found, it supports my expectation that higher education and income correlate with greater social trust, aligning with existing literature (Putnam, 2000; Uslaner, 2002). If not, I will consider other factors that might influence trust, such as environmental or cultural variables, which could explain the lack of a significant association.
References
Putnam, R. D. (2000). Bowling alone: The collapse and revival of American community. Simon & Schuster.
Uslaner, E. M. (2002). The moral foundations of trust. Cambridge University Press.
