8210 wk4 discussion
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Response 1
Leila Abouzaki
RE: Discussion - Week 4
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General Social Survey Dataset
Visual displays of data can be invaluable because it makes it easier to understand the statistical findings through visual representation (Walden University, 2016). SPSS software allows the drawing of a sample from a dataset which can be performed to take a random or targeted sample (Wagner, 2020). In the General Social Survey Dataset, the older population's mean of the age in the dataset is 49.01 likely implying there are older respondents in the population. The median is the "middle score" of 49.00 which would make the data normally distributed, however, the level of skewness is positive which makes the data skewed slightly to the right. Thus, the mean indicates the results may not be generalizable across all age groups. I chose to display the data surrounding the age of the respondents.
Confidence Interval for Sample of 100 of Respondents' Reported Age
A random sample of 100 respondents was taken from the age of the respondents to determine the likelihood of an interval containing the parameters of the population's age. The confidence level is the likelihood or percentage of a probability that a specified interval will contain a population parameter (Frankfort-Nachmias et al., 2020). Using a sample of 100 (N = 100) out of 500 respondents for the respondent's reported age, the 95% confidence level has a range of values showing a lower bound of 44.52 and an upper bound of 51.24 (table 1) which is wider than the 90% confidence level between 45.07 and 50.69. Table 1 shows there is a 95% chance that the respondents' reported age is between the upper and lower bounds. Thus, the upper and lower bounds are the boundaries of stated values that show the likelihood in which constrainted or limited values lie (Wagner, 2020).
Table 1
Respondents' Reported Age
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Descriptives |
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Statistic |
Std. Error |
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AGE OF RESPONDENT |
Mean |
47.88 |
1.693 |
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95% Confidence Interval for Mean |
Lower Bound |
44.52 |
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Upper Bound |
51.24 |
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5% Trimmed Mean |
47.39 |
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Median |
49.00 |
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Variance |
286.531 |
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Std. Deviation |
16.927 |
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Minimum |
19 |
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Maximum |
89 |
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Range |
70 |
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Interquartile Range |
27 |
|
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Skewness |
.244 |
.241 |
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Kurtosis |
-.804 |
.478 |
Confidence Interval for Sample of 400 of Respondents' Reported Age
A random sample of 400 respondents was taken from the age of the respondents to determine the likelihood of an interval containing the parameters of the population's age. Using a sample of 400 out of 500 respondents, the 95% level of confidence was between 46 and 49.35 (table 2) is slightly wider than a 90% confidence between 46.27 and 49.08. When the sample size is increased from 100 to 400, the width of the confidence interval (CI) decreases to 44.52 and 51.24 (table 2). Consequently, table 2 shows the standard error of the mean has decreased in value to .850. When the width of CI decreases so does the probability that the specified interval will contain a population of respondents' age parameter and thus, the possibility of standard error decreases.
Table 2
Respondents' Reported Age
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Descriptives |
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Statistic |
Std. Error |
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AGE OF RESPONDENT |
Mean |
47.68 |
.850 |
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95% Confidence Interval for Mean |
Lower Bound |
46.00 |
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Upper Bound |
49.35 |
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5% Trimmed Mean |
47.16 |
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Median |
46.00 |
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Variance |
287.721 |
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Std. Deviation |
16.962 |
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Minimum |
18 |
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Maximum |
89 |
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Range |
71 |
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Interquartile Range |
25 |
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Skewness |
.339 |
.122 |
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Kurtosis |
-.654 |
.244 |
“Confidence Intervals Are Underutilized”
Confidence intervals are underutilized because sometimes a social science research hypothesis provides insignificant difference between what is being measured and the sample error. One implication might be of using confidence intervals is COVID-19 vaccine efficacy rates such as the Pfizer vaccine efficacy rate. Within Confidence Intervals of COVID-19 vaccine efficacy rates, Wang (2021) used publicly available data from drug makers and the Food and Drug Administration (FDA) to guide learners to estimate the confidence intervals of COVID-19 vaccine efficacy rates. The Pfizer vaccine distribution allowed one to talk about the probability of the parameter, which is often more natural when communicating uncertainty (Wang, 2021). The results showed that there is a 95% probability that Pfizer’s vaccine efficacy rate is between 90.3% and 97.6%, based on the clinical trial data (Wang, 2021). The probability of the unknown parameter can be graphed, and students can use it to communicate confidence intervals more flexibly (Wang, 2021). Therefore, the confidence intervals were similar to classical ones reported in medical literature and the probability of vaccine efficacy rates was similar to that of Pfizer scientists during the FDA meeting (Wang, 2021).
Conclusion
The implication for confidence intervals can show that even if the efficacy rate is only 70%, for every 100 people who become infected by COVID-19 in the unvaccinated community, there will be on average 30 sick people in the vaccinated community (Wang, 2021). 95% confidence is a confidence interval that will include the population mean and a statement about the entire algorithm and not a single CI (Magnusson, n.d.). Moreover, CI can be found in just about any field of study (Walden University Library, n.d.).
References
Frankfort-Nachmias, C., Leon-Guerrero, A., & Davis, G. (2020). Social statistics for a diverse society (9th ed.). Sage Publications.
Magnusson, K. (n.d.). Welcome to Kristoffer Magnusson’s blog about R, Statistics, Psychology, Open Science, Data Visualization [blog]. http://rpsychologist.com/index.html
Wagner, III, W. E. (2020). Using IBM® SPSS® statistics for research methods and social science statistics (7th ed.). Sage Publications.
Wang, F. (2021). Confidence Intervals of COVID-19 vaccine efficacy rates. Numeracy: advancing education in quantitative literacy, 14(2), 1–19. https://doi.org/10.5038/1936-4660.14.2.1390
Walden University Library. (n.d.). Course Guide and Assignment Help for RSCH 8210. http://academicguides.waldenu.edu/rsch8210
Walden University, LLC. (Producer). (2016). Visual displays of data [Video file]. Author.
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RESPONSE 2
Kristin Domville
RE: Discussion - Week 4
Top of Form
General Social Survey Dataset
In the General Social Survey Dataset, data entered for the multiple variables provides the social scientist with a wide range of data on participants' characteristics, attitudes, and behaviors. The mean age of the sample size of 100 participants is 49.00 years; this indicates that data results are specific to the behaviors and characteristics of a middle-aged individual and may not be generalizable across all age groups. In a larger sample size, N=400, the mean age of the participants drops to 47.86 years of age. This indicates that most of the participants were around 47.86 years of age. By increasing the sample size, there is an increased estimation of the participant's mean age.
According to Frankfort-Nachmias et al., (2020), the confidence level is the probability that the population parameters will fall between the values surrounding the mean. The confidence interval of the variable, family income, was calculated for a sample size of 100 respondents and 400 respondents out of 500 respondents.
Confidence Interval Sample of 100 Respondents' Family Income
In table 1, Confidence Interval N=100, when the N= 100, the width of the 95% confidence interval with a standard error of +/-1.96 (5156.13) =10,106.37 indicating a range between $40,779.41 to $61,280.67. Out of the 100 respondents, the data indicates that the average salary is 51, 028.54. The confidence interval of 95% states that there is a probability that the family income value of the sample of 100 will fall between the upper bound of $61,280.67 and the lower bound of $40,776.41. There is a 5% chance that a sample would be outside the family income confidence interval.
The sample size of 100 out of 500 respondents was used to calculate the 90% confidence interval. There was a standard error of $5,156.313 with a 90% confidence interval range of $42,453.70 – $59,603.38. The statistical significance indicates that there is a 10% chance the population's family income will be below $42,453.70 or above $59,603.38. The 95% confidence interval indicates a wider range of family income values compared to the 90% confidence level.
Table 1
Confidence Interval N=100
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Confidence Interval Sample of 400 Respondents' Family Income
In table 2, Confidence Interval N=400, when the N= 400, the width of the 95% confidence interval with a standard error of +/-1.96 (2745.018) = 5,380.24 indicating a range between $55,249.13 to $66,046.01. Out of the 400 respondents, the data indicates that the average salary is $60,647.57. The confidence interval of 95% states that there is a probability that the family income value of the sample of 400 will fall between the upper bound of $66,046.01 and the lower bound of $55,249.13. There is a 5% chance that a sample would be outside the family income confidence interval.
The sample size of 400 out of 500 respondents was used to calculate the 90% confidence interval. There was a standard error of 2,745.018 with a 90% confidence interval range of $56,120.67-$65,174.47. The statistical significance indicates that there is a 10% chance the population's family income will be below $56,120.67 or above $65,174.41. When compared to the N=100 the standard error of the mean decreased by $2,411.30.
Table 2
Confidence Interval N=400
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Descriptive |
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Statistic |
Std. Error |
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FAMILY INCOME IN CONSTANT DOLLARS |
Mean |
60647.57 |
2745.018 |
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95% Confidence Interval for Mean |
Lower Bound |
55249.13 |
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Upper Bound |
66046.01 |
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5% Trimmed Mean |
58333.47 |
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Median |
49882.50 |
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Variance |
2697573519.299 |
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Std. Deviation |
51938.170 |
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Minimum |
370 |
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Maximum |
160742 |
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Range |
160373 |
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Interquartile Range |
68358 |
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Skewness |
.907 |
.129 |
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Kurtosis |
-.420 |
.257 |
In conclusion, sample size affects the confidence interval since it changes the standard error of the variable. Increasing the sample size decreases and width of the confidence interval and decreases standard error. Conversely, decreasing the sample size increases the confidence interval's width and the standard error. When the N was increased to 400, the width of the 95% confidence interval decreased to 55249.13 to 66,046.01 or 10,796.88 (standard error=2745.018) and with 90 % confidence to 56,120.67 – 65,174.47 or 9,053.80 and standard error of 2,745.018.
Confidence Intervals are Underutilized
In the article, Using Intrusive Advising to Improve Student Outcomes in Developmental College Courses, confidence intervals were used to determine the proportion of students who passed a strong-start developmental math course compared to an instructor-matched developmental math course. It was determined that the 95% confidence interval of students passing a Strong-Start supported math course was significantly greater (1.9 times) than students passing an unsupported instructor-matched math course (Thomas, 2020).
Confidence intervals are necessary because the interval describes the chances that the variable lies within the interval or, conversely, the risk that the interval does not fall in the interval. Confidence intervals are underutilized in social science research since there is a common misunderstanding that the interval means that that percentage of data falls between the upper and lower bound. I think that social science frequently has smaller N values, and the standard error may be high for the smaller sample sizes.
References
Frankfort-Nachmias, C., Leon-Guerrero, A., & Davis, G. (2020). Social statistics for a diverse society (9th ed.). Thousand Oaks, CA: Sage Publications.
Thomas, N. (2020). Using intrusive advising to improve student outcomes in developmental college courses. Journal of College Student Retention: Research, Theory, & Practice 22(1) 251-272.
https://doi:10.1177/1521025117736740
Wagner, III, W. E. (2020). Using IBM® SPSS® statistics for research methods and social science statistics (7th ed.). Thousand Oaks, CA: Sage Publications.
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