Stat200: Chapter 1 Working With Data

Front 1

A collection of procedures and principles for gathering data and analyzing information to help people make decisions when faced with uncertainty

Back 1

Definition of Statistics I

Front 2

The mathematics of the collection, organization, and interpretation of numerical data, especially the analysis of population characteristics by inference from sampling

Back 2

Definition of Statistics II

Front 3

The art and science of gathering and analyzing information in order to draw conclusions about a larger population

Back 3

Definition of Statistics III

Front 4

The plural of anecdote;

Groups of information that represent the qualitative or quantitative attributes of a variable or set of variables

Back 4

Data

Front 5

A collection of individuals about which information is desired

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Population

Front 6

individuals are observed; opposed to experimental statistics

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Observable Statistics

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study in which the individuals are assigned

Back 7

Experimental Statistics

Front 8

a characteristic of an individual that can be measured

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Variable

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the individual, also called the sample unit, or the observation

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Observable Unit

Front 10

the number of observational units for which we have collected data

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Sample Size

Front 11

a measure summarizing some characteristic of the population

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Parameter

Front 12

a measure based solely on observable data that approximates a population parameter

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A Statistic

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Identifies a quality of an individual;

The only applicable mathematical operator is “=“

E.g., Male/Female; Red/Green/Blue; Yes/No

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Nominal

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Ranks or orders, but has no fixed interval.

<, >, = apply, but not addition, subtraction, etc.

E.g., Approve/Neutral/Disapprove; SRTE evaluations

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Ordinal

Front 15

Nominal & Ordinal

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Categorical Variables

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Interval & Ratio

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Quantitative Variables

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Gradations on regular intervals, but with an arbitrary zero point

Now we can add and subtract, but not multiply or divide

E.g., temperature as measured in Fahrenheit or Celsius

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Interval

Front 18

The most common – regular intervals and a fixed zero point

Multiplication and division is possible

E.g., household income, height, calories

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Ratio

Front 19

Frequency; Relative Frequency; A Pie Chart & Bar Graph

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Ways of working with one categorical variable

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describes how many observations fell into each category

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Frequency

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describes the proportion or percent of the sample (population) that falls into each category.

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Relative Frequency

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ex. "How often do you use seatbelts while driving?" (People in general)

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One Categorical Variable

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what does one variable (explanatory) tell us about the other (response)?

Relative Frequency; Contingency Table; Bar Graph

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Working with 2 Categorical Variables

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Describes the proportion or percent of each explanatory variable that falls into each category of response

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Relative Frequency (2 Categorical Variables)

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The two-way table of categorical values

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Contingency Table

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"How often do you use seatbelts while driving?" (Female vs. Male)

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2 Categorical Variables

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individual observations of n samples of random variable

the (mean) of the population is estimated from the average of sample values

median

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Working with 1 Quantitative Variable

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the individual observations of (n) samples of a random variable

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X1, X2, X3, …, Xn

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Average of the sample values

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x = E Xi / n

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How the mean (center) of the population is estimated

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From the average of the sample values

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The spread is estimated by

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The Range; Variance; Standard Deviation

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Max (Xi) - Min (Xi)

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The Range

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v = E (xi - x*) ^ 2 / n-1

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The Variance

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s = (radical) V

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The Standard Deviation

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two modes

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bimodal

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To make a random variable fit the normal distribution we use..

Z = (observed - mean) / standard deviation

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Standardized Scores

Front 37

Use Regression to create an equation

Y = a + bX
ex. Weight = -318 + 7* Height

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Working with 2 Quantitative Variables

Front 38

Quantitative and Qualitative (Categorical) Data Combined

Back 38

Analysis of Variance