Chapter 1

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Why learn Statistics

• Helps understand articles

• Helps with personal research

• Improves reasoning and Intuition

• Makes you a better consumer of science

What are Statistics

• Statistics is a branch of applied mathematics focusing on the organization, analysis, and interpretation of group of numbers or large amounts of data.

• There are two main branches

  • Descriptive

    • Summarizes a group of numbers form a research study

      • Provide averages, graphs, tables, etc

    • The numerical, graphic, and tabular descriptions or output of collected data

  

  • Inferential

    • Methods and procedures for drawing conclusions, make inferences based on scores collected in a research study and going beyond them

      • Generalizations from sample to population

      • Samples (statistics) vs. Populations (Parameters: Unknown)

    • Statistics are the TESTS that can be used to analyze collected data

      • t-est

        

      • Z-test

Populations and Samples

• Population

  • Total set of subjects of interest (all TAMIU students)

• Sample

  • Representative subset of the bs

Theory and Research

• Theory

  • Organized system of assumptions/principles that attempts to explain certain phenomena and how they are related

    • Guides research

    • Karl Popper: Look!Look!

      • telling someone to look without telling them where

    • Frames of Reference: Ways of looking at research questions/ problems/ motivation

    • Hypothesis: Prediction

Variables

• Variable

  • Characteristic/ condition that can have different values

    • Gender, Ethnicity, Religiosity

• Value

  • Possible number or category a score can have

    • Rating scale: 1-10; Gender: F vs. M; F=1 vs. M=0

• Score

  • A particular person’s value

    • e.g., values on a test 70, 80, 90

• Discrete (Nominal, Qualitative variable):

  • Fixed values (Categorical, subcategories)

    • Religion: (Catholic, Protestant)

    • Political party: (Republican, Democrat, Independent)

    • Gender: Male, Female

    • Numbers no Numerical value: Male = 1, Female = 2

• Continuous (Numeric, quantitative variable)

  • Infinite or unlimited values

  • Age: in years, 2.3 years old, 3.5 days old child

Discrete and Continuous Variables

• Discrete and Quantitative!!

  • Variables that only take on values from a set of separate numbers

    • Number of crimes committed

      • can you have 1.5 or 1.8 crimes)

    • Number of elections previously voted in

      • Voted 1.5 times?

    • Number of children

      • Household = 1.5 children/ family

Assumptions Underlying Statistical Procedures

• Randomization

  • Random selection

  • Random assignment

• Sample size

Scales or Levels of Measurement

• Nominal: variable in which values are categories

  • Ex) Gender, religion, ethnicity

• Ordinal (rank-order): numeric values correspond to the relative position of things measured

  • Ex) class rank or birth order

Scales or Levels of Measurement

• Interval

  • Numeric, quantitative and continuous

  • Ages: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65

    • Continuum of ages: Equal distance intervals

  • Equal unit size or interval: Units of measurements (intervals) on scale are all equal in size

    • Distance between 5 and 10 identical to 60 and 65

    • Temperatures: Difference between 30 degrees and 40 degrees same as differences between 80 degrees and 90 degrees

  • Underlying numerical information provided by measure

    • Equal-interval: Numeric Variable (No absolute ZERO)

• Carries identity: Days with different temps receive different scores on scale

• Magnitude: (cooler days receive lower scores)

• Equal unite size: differences between values correspond to differences in the underlying thing being measured (Diff. b/n 20 degrees & 40 degrees is equivalent to the difference of 50 degrees & 70 degrees)

  • Ex) pain level, stress level, ratings of mood, age

• Ratio

  • Identical to interval with one exception

    • it has an absolute zero

    • ZERO stands for the absence of something.

      • Temperature in K (0K = - 459.67 F!)

      • F or C Temperatures can go below ZERO

      • Time, weight

      • Income: Persons can have no money? Is it a ratio?

        • Technically both

Key Points

• Descriptive statistics are used to describe and summarize a group of numbers from a research study

• A value: is a number or category; a variable is a characteristic that can have different values; a score is a particular person’s value on the variable.

• Some numeric variables are rank-ordered and some variable are names or categories and not numbers