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introduction to Statistics and Statistical Thinking

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Overview
• Collecting and Measuring Data
• What Is Statistics?
• The Purpose of Statistics
• Inferential Statistics
• Types of Data
• Applications of Statistics
• Fundamentals of Statistics
• Critical Thinking
• Experimental Design
• Random Samples

More to come
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Collecting and Measuring Data
• Ratio measurements provide the greatest flexibility in statistical methods that can be used for analyzing the data.
• Interval data allows for the degree of difference between items, but not the ratio between them.
• Ordinal measurements have imprecise differences between consecutive values, but have a meaningful order to those values.
• Variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically, they are often grouped together as categorical variables.
• Ratio and interval measurements are grouped together as quantitative variables.
• Nominal measurements have no meaningful rank order among values.

What Is Statistics?
• Statistics combines mathematical and non-mathematical procedures into one discipline.
• Statistics is generally broken down into two categories: descriptive statistics and inferential statistics.
• Statistics is an applied science and is used in many fields, including the natural and social sciences, government, and business.
• The use of statistical methods dates back to at least the 5th century BC.

The Purpose of Statistics
• Statistics is an extremely powerful tool available for assessing the significance of experimental data and for drawing the right conclusions from it.
• Statistics helps scientists, engineers, and many other professionals draw the right conclusions from experimental data.
• Variation is ubiquitous in nature, and probability and statistics are the fields that allow us to study, understand, model, embrace and interpret this variation.

Inferential Statistics
• Inferential statistics is used to describe systems of procedures that can be used to draw conclusions from data sets arising from systems affected by random variation, such as observational errors, random sampling, or random experimentation.
• Samples must be representative of the entire population in order to induce a conclusion about that population.
• Statisticians use tests of significance to determine the probability that the results were found by chance.

Types of Data
• Primary data is data collected first-hand.Secondary data is data reused from another source.
• Qualitative data is a categorical measurement expressed not in terms of numbers, but rather by means of a natural language description.
• Quantitative data is a numerical measurement expressed not by means of a natural language description, but rather in terms of numbers ([[fig:17691]]).

Applications of Statistics
• Statistics can be used to improve data quality by developing specific experimental designs and survey samples.
• Statistics includes the planning of data collection in terms of the design of surveys and experiments.
• Statistics provides tools for prediction and forecasting and is applicable to a wide variety of academic disciplines, including natural and social sciences, as well as government, and business.

Fundamentals of Statistics
• For practical reasons, a chosen subset of the population called a sample is studied—as opposed to compiling data about the entire group (an operation called census).
• <em>Descriptive statistics</em> summarizes the population data by describing what was observed in the sample numerically or graphically.
• <em>Inferential statistics</em> uses patterns in the sample data to draw inferences about the population represented, accounting for randomness.
• Statistical analysis of a data set often reveals that two variables (properties) of the population under consideration tend to vary together, as if they were connected.
• To use a sample as a guide to an entire population, it is important that it truly represent the overall population.

Critical Thinking
• Statistics can be made to produce misrepresentations of data that may seem valid.
• Statistical literacy is necessary to understand what makes a poll trustworthy and to properly weigh the value of poll results and conclusions.
• Critical thinking is a way of deciding whether a claim is always true, sometimes true, partly true, or false.
• The list of core critical thinking skills includes observation, interpretation, analysis, inference, evaluation, explanation, and meta-cognition.

Experimental Design
• The experimenter is often interested in the effect of some process or intervention (the “treatment”) on some objects (the “experimental units”), which may be people, parts of people, groups of people, plants, animals, etc.
• A methodology for designing experiments involves comparison, randomization, replication, blocking, orthogonality, and factorial considerations.
• It is best that a process be in reasonable statistical control prior to conducting designed experiments.
• One of the most important requirements of experimental research designs is the necessity of eliminating the effects of spurious, intervening, and antecedent variables.

Random Samples
• Simple random sampling merely allows one to draw externally valid conclusions about the entire population based on the sample.
• Advantages of random sampling are that it is free of classification error, and it requires minimum advance knowledge of the population other than the frame.
• Simple random sampling best suits situations where not much information is available about the population and data collection can be efficiently conducted on randomly distributed items, or where the cost of sampling is small enough to make efficiency less important than simplicity.

Appendix

Key terms
• critical thinking the application of logical principles, rigorous standards of evidence, and careful reasoning to the analysis and discussion of claims, beliefs, and issues
• dependent variable in an equation, the variable whose value depends on one or more variables in the equation
• empirical verifiable by means of scientific experimentation
• experiment A test under controlled conditions made to either demonstrate a known truth, examine the validity of a hypothesis, or determine the efficacy of something previously untried.
• independent variable in an equation, any variable whose value is not dependent on any other in the equation
• inferential statistics A branch of mathematics that involves drawing conclusions about a population based on sample data drawn from it.
• population a group of units (persons, objects, or other items) enumerated in a census or from which a sample is drawn
• population a group of units (persons, objects, or other items) enumerated in a census or from which a sample is drawn
• population a group of units (persons, objects, or other items) enumerated in a census or from which a sample is drawn
• population a group of units (persons, objects, or other items) enumerated in a census or from which a sample is drawn
• population a group of units (persons, objects, or other items) enumerated in a census or from which a sample is drawn
• primary data data that has been compiled for a specific purpose, and has not been collated or merged with others
• qualitative data data centered around descriptions or distinctions based on some quality or characteristic rather than on some quantity or measured value
• quantitative of a measurement based on some quantity or number rather than on some quality
• random sample a sample randomly taken from an investigated population
• sample a subset of a population selected for measurement, observation, or questioning to provide statistical information about the population
• sample a subset of a population selected for measurement, observation, or questioning to provide statistical information about the population
• sample a subset of a population selected for measurement, observation, or questioning to provide statistical information about the population
• sampling the process or technique of obtaining a representative sample
• statistical literacy the ability to understand statistics, necessary for citizens to understand mateiral presented in publications such as newspapers, television, and the Internet
• statistics a mathematical science concerned with data collection, presentation, analysis, and interpretation
• statistics The study of the collection, organization, analysis, interpretation, and presentation of data.
• variable a quantity that may assume any one of a set of values

Quantitative Data
The graph shows a display of quantitative data.

Linear Regression in Inferential Statistics
This graph shows a linear regression model, which is a tool used to make inferences in statistics.

Random Sampling
MIME types of a random sample of supplementary materials from the Open Access subset in PubMed Central as of October 23, 2012.The colour code means that the MIME type of the supplementary files is indicated correctly (green) or incorrectly (red) in the XML at PubMed Central.

Critical Thinking
Critical thinking is an inherent part of data analysis and statistical literacy.

Old-fashioned scale
A scale is emblematic of the methodology of experimental design which includes comparison, replication, and factorial considerations.

The Purpose of Statistics
Statistics teaches people to use a limited sample to make intelligent and accurate conclusions about a greater population.The use of tables, graphs, and charts play a vital role in presenting the data being used to draw these conclusions.

Summary statistics
In descriptive statistics, summary statistics are used to summarize a set of observations, in order to communicate the largest amount as simply as possible.This Boxplot represents Michelson and Morley’s data on the speed of light.It consists of five experiments, each made of 20 consecutive runs.

Defining a population
In applying statistics to a scientific, industrial, or societal problem, it is necessary to begin with a population or process to be studied. Populations can be diverse topics such as “all persons living in a country” or “all stamps produced in the year 1943”.

Attribution
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