Running Header: Basic Statistics Walker 2
Essay II: Basic Statistics Assignment
Leon J. Walker
EDCO 735
Dr. Volk
September 2, 2021
Basic Statistics
When it comes to statistical data evaluating the information may not always be about final figure. In some instances, scientists must also make judgement calls to make sure there is no skewing of the data in anyway, shape or form. Posted below is a visual example of how data can be misconstrued because the statistician relied on the final number instead of their judgement regarding outliers in our data. An example of when the data is unintentionally skewed because of the outliers are examining the salaries of staff in a school.
Staff 1
Staff 2
Staff 3
Staff 4
Staff 5
Staff 6
Staff 7
Staff 8
$29,000
$30,000
$35,980
$39,500
$32,950
$33,900
$110,000
$102,500
In this scenario, the mean salary would $47,231.25. But, after taking a closer look at the raw data. Calculating and using the mean is not always the best way to report this data if the statistician is looking for accuracy. The salary of a typical school staff worker lies between $29,000 and $39,000. The average is being distorted by the two outlier salaries.
For the sake of identifying and resolving the repercussions of the outliers have in data it is essential to graph the data in the form of a histogram so that the form of the data can be revealed. When we study a histogram if the majority of the data is located on the left side and the finite greater numbers on the right, it means the data is skewed right. Greater numbers actually do affect the mean; however, it does not affect the median. On a histogram the majority of the data is to the right, along with a few smaller values showing up on the left side of the histogram. Meaning that the data is skewed to the left. Lesser values bring the overall mean down. Once again, this minimally affects the median. Symmetric data is when a median and mean are close to each other, which would give the histogram a form near the same in either side of the middle (Kwak & Kim, 2017).
The sum of squares measures howe spread out a set of measures are. Additionally, the sum of the squares, which is sometimes indicated by SS, provides a measure that is simple to calculate and use (Warner, 2021). Posted below us and example using the data set above to find the SS in excel.
The sum of the squares (SS) is a sum of squared deviations of scores concerning a mean that produces data at the variability. SS appears in the formulas for many more advanced statistical analyses (SS = (X – M). SS terms are the foundation for the ANOVA and multiple Ʃ ᵢ regression. For SS to equal 0, the set of X terms being evaluated must all be identical, therefore, cannot be negative. When the variability between X scores increases, SS becomes larger. The value of SS has no upper limit. Squaring a deviation must yield a possible number (Warner, 2021).
Sampling distributions form the theoretical foundation for confidence interval construction and hypothesis testing. A sampling distribution is an outcome that has been gathered from thousands of random samples that has taken from a population and using a statistic, e.g., M will be used to calculate for every sample (Wagenmakers, Marsman, Jamil, 2018). When distinguishing a t-distribution from a standard normal distribution. The curves do the t-distribution and normally distributed different like N (the number of participants in a sampling) and df declines that make the t distribution turned into a flatter in the center. N can significantly affect the Confidence Intervals (Cis). Just like when collecting any data when testing a hypothesis, a scientist must be able to collect real and the true demographic mean (Bornmann, 2017).
References
Bornmann, (2017). Confidence intervals for Journal Impact Factors. Scientometrics 111, 1869– 1871. https://doi.org/10.1007/s11192-017-2365-3
Kwak, S., & Kim, J. (2017). Statistical data preparation: management of missing values and outliers. Korean Journal Of Anesthesiology, 70(4), 407. doi: 10.4097/kjae.2017.70.4.407
Wagenmakers, EJ., Marsman, M., Jamil, T. et al. (2018). Bayesian inference for psychology. Part I: Theoretical advantages and practical ramifications. Psychon Bull Rev 25, 35–57. https://doi.org/10.3758/s13423-017-1343-3
Warner, R. M. (2021). Applied statistics I: Basic bivariate techniques (3rd ed.). Thousand Oaks, CA: Sage Publications. ISBN: 978-1-5063-5280-0.
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