FSR- Statistical Reasoning Module Overview

 Statistical Reasoning Overview

Introduction

Statistical reasoning is the process of learning from data. You can learn from data concerning 9th graders' lunch preferences or the number of cats older people own. All industries can learn something from data. Scientists, businesses, politicians, sports analysts, and hundreds of other different fields use data to ask and answer questions. Some of the techniques used to learn about the world from data are exploring data sets, using statistics and data visualizations to identify patterns and make predictions. Ultimately statistical reasoning is used to explore a data set or sample of data and can be used make predictions and draw reliable conclusions about the world. 

Lesson Preview

In this module, we will study the following topics:

Statistical Investigations: Learn how to explore questions and make predictions using data sets. 

Data Measures: Explore different measures of central tendency, which attempt to find the center of a data set. 

Line Graphs, Bar Graphs, and other Data Displays: Use charts, graphs, and visualizations to help bring meaning and understanding to otherwise complex data. 

Correlation: Take a look at how data can provide a trend that you can use to predict the future! 

Stock Market Graphs: Explore how investors take a lot of fluctuating data and make inferences.

Key Terms

The following key terms will help you understand the content in this module.

  • 5-Number Summary - A summary for a variable consisting of the minimum, the lower quartile, the median, the upper quartile, and the maximum number.
  • Bias - Any systemic failure of a sampling method to represent its population.
  • Biased Statistic - When the statistic of an expected value does not equal the parameter or quantity estimated.
  • Boxplot - Displays the 5-number summary as a central box with whiskers that extend to the non-outlying data values.   Boxplots are particularly effective for comparing groups of different sizes.
  • Candlestick Chart/ Stock Bar Chart – a style of bar chart used primarily to describe price movements of a security, derivative, or currency over time
  • Census - A sample that consists of the entire population.
  • Control Group - Randomly assigning participants to receive a fake treatment helps control for the placebo effect.
  • Correlation - An association between two variables.
  • Correlation Coefficient - Represented by r, it is a number between -1 and 1, inclusive, that is used to judge how closely a line fits the data.
  • Double-Blind - Studies conducted where the control group is unknown to the researcher and the participants.   Participants sometimes inaccurately report their improvement.   Likewise, researchers sometimes subconsciously try harder to find improvement in treatment-group participants versus control-group participants.
  • Experimental Study - Research in which the researcher separates the participants into at least two groups, applies some sort of treatment, and then compares results.
  • Frequency - The count or number of times an event occurs
  • Histogram - Uses adjacent bars to show the distribution of values in a quantitative variable.   Each bar represents the frequency of values falling in an interval of values.
  • Hypothesis - A formal research question.
  • Quartile - The median and the quartiles divided data into four equal parts.
  • Mean - Found by summing all the data values and dividing by the count.
  • Median - The middle value of an organized data set, with half of the data above and half below it.
  • Negative Correlation - When the value of one variable decreases as the other variable increases.
  • Observational Study - Research in which data is collected about some characteristic(s) of the population.   The data can be collected by observation or by a survey or interview.
  • Outlier - Extreme values that don't appear to belong with the rest of the data.   They may be unusual values that deserve further investigation, or just mistakes; there's no obvious way to tell.
  • Positive Correlation - A relationship where the value of one variable increases as the other variable increases.
  • Placebo - A treatment known to have no effect, administered so that all groups experience the same conditions.
  • Placebo Effect - The tendency of many human subjects (often 20% or more of the experiment subjects) to show a response even when administered a placebo.
  • Range - The difference between the lowest and highest values in a data set.
  • Sample - A (representative) subset of the population, examined in hope of learning about the population.
  • Scatterplot - A graph that shows the relationship of bivariate data using points on the coordinate grid.
  • Simple Moving Average – an average of a stock over a specific time period
  • Smoothing Techniques – a technique that indicates an underlying trend
  • Statistic - Statistics are values calculated for sampled data.

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