Statistical Concepts: Seven Pillars of Statistics

• Session 1 and 2 explored key concepts and pillars of statistics.

Seven Pillars of Statistics

• Aggregation involves finding the mean or average from observations.
• Information (information measurement) pertains to how data can be measured.
• Accuracy is related to the amount of data.
• Likelihood calibrates inferences using probability.
• Intercomparison makes statistical comparisons within the data itself, rather than against an external standard.
• Regression is essentially a bivariate normal distribution.
• Design refers to the design of experiments.
• Residual is a catch-all category, encompassing "everything else."

Oversimplification

• The study focuses on the value of targeted data reduction or compression.
• Increased amounts of data have a diminishing value.
• Probability measuring is essential.
• Consider internal variation of data to help ensure accuracy.
• Asking questions from different perspectives can reveal different answers.
• Planning observations plays a large logistical role.
• These steps facilitates the exploration and comparison of competing explanations in science.

Aggregation (Chapter 1)

• Aggregation is the "combination of observations."
• Statisticians discard some data information when taking a mean.
• Averages used to highlight the contrast, specifically "before minus after”.
• Midrange calculates the mean of the largest and smallest values.
• The challenge is how to summarize similar, but not identical, sets of measurements, an issue that still persists.
• The method of least squares is a weighted average of observations and had the advantage over methods of being easily extendable to more complicated situations to determine more than two unknowns.
• Using summaries in place of full enumeration of individual observations helps gain information by selectively discarding information.
• Statistics, specifically aggregation/finding the mean of observations, applies across disciplines and can help formulate policies.

Information (Chapter 2)

• Information measurement is related to combining observations to gain information.

• It focuses on how the gain is related to the number of observations.

• It asks how to measure the value and acquisition of information.

• Laplace reached the same conclusion regarding the total or mean of observations, where individual observations followed almost any distribution.

• The main theme of this chapter is the effect of correlation on the amount of information in the data.

• The concept that information in data could be measured and that accuracy was related to the amount of data was established by 1900.

• Sources claimed that in some situations, it is better to discard one of two observations than to average them.

• The statistical assessment of information accumulation is complex.

• The measurement of information in data, the comparative information in different datasets, and the rate of increase in information with an increase in data has become a pillar of statistics.

• Measurement of information involves using statistics to analyze correlation with consideration of the study group size and increase in numbers with more data.

• Consider the objective of the study.

• Journal 1 focuses on Aggregation and is due 2/10.

• The impact of Tulsa's regional demographics provides a snapshot of the city's demographics and baseline general statistics.

• The 9b Neighborhood explorer focuses on trend differences over time.

• The Equality indicator highlights the most disadvantaged group and compares it to the most advantaged group.

• Systemic disparities effectively show differences between groups by incorporating range in calculations, distinguishing themselves the other 2 orgs.