Module 1 - Statistical Preliminaries

What is Statistics?​

• A science that deals with the collection, organization, analysis, & interpretation of numerical data.

  • May look like satisfaction surveys, ​

• All the procedures & tools used to organize and interpret facts, events, & observations that can be expressed numerically.​

• Numerical facts that summarize large groups of people.​

• Allow for explanation, comparison, and exploration of everyday phenomena.​

• Allows us to make conclusions about experiences in our world.

Social Science Research​

• Understanding statistics is useful in answering questions such as the following:​

• What kind of data should be collected?​

• How much data to provide accurate guidance?​

• How should I organize these data?​

• How can I organize the data and draw conclusions?​

• How can we access the strength of the conclusions?

Goals of this class​

• Learn basic vocabulary, procedures, and logic.​

• Become a better everyday consumer of statistical information​

• Have the tools to calculate and interpret statistics on data you or others collect.​

• Improve ability to read and understand professional literature in the behavioral sciences.

Why do we study Statistics?

• ​For Research.

  • Answer Questions​

  • Analyze Data​

  • Interpret Results

Basic Vocabulary

• Variable​

  • anything that can take on different values or amounts over a period of time.​

• Independent Variable → “The Influencer”​

  • the variable that is manipulated, (or controlled), by the researcher.

    • manipulation is to break something down

      • Contributes to the organization of the data. ​

• Dependent Variable → “The Influencee”​

  • the variable that the researchers observe to see if it changes due to the changes in the independent variable. It is the data we analyze.

    • It is what we watch (to see how we played with the indep. vari.)

• ​Discrete Variable —> “Finite”​

  • finite number of values for a specific variable.​

    • Example: Gender​

• Continuous Variable—>”Infinite”​

  • theoretical infinite number of values between any two points.​

    • Example: Height or weight

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Basic Statistical Terms

• Descriptive Statistics​

  • Using statistics to describe, summarize, and organize data. ​

    • Simple ways to describe & understand data but does not go beyond the data.

    • CANNOT make inference beyond its sample of data​

      • Example: average test score in your class​

• Inferential Statistics​

  • Draws conclusions → makes inferences about a population based on sample.

    • ​makes inferences about a population based on a sample.

    • Can also be used to compare groups using statistical index, or

    • Calculates error as well in addition to sample (aka estimate)

      • Example: does the color of a toothpaste affect toothpaste preference​

Scales of Measurement

• Nominal Scale: ​

  • It is a piece of data labeled with a name or label for different objects (or events)​

    • Example: Room numbers in a school, Social Security number.

• Ordinal Scale:​

  • Ranking data. Tells us the ranking, or rank ordering of each object or event.

    • In addition, carries information about ordering in a particular sequence.

      • Example: Order of finish in a race.

• Interval Scale:​

  • Each unit is assumed to be equal to each other unit on the scale.​

    • Not only arrange observations according to their magnitude but also distinguish the ordered arrangement in equal units.​

      • For example: Temperature (Celsius) → You can have a temp of 0 because it is apart of scale​.

• Ratio Scale:​

  • Contains all the characteristics above with one addition: A true zero.​

    • For example: Income

      • True zero = “absence of” (represents NO information)

Measurement Variables​

• Quantitative:​

  • Quantity variable (Numerical)

    • A variable representing the ordinal, interval, or ratio scales​

• Qualitative:​

  • Quality variable (Categorical)

    • A variable measured on the nominal scale