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Data and Statistics

Chapter 1BA 201 – Fall 2010

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Statistics

Numerical facts such as averages, medians, percents, and index numbers.

Art and science of collecting, analyzing, presenting, and interpreting data.

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Data and Data Sets

Data are the facts and figures collected, analyzed, and summarized for presentation and interpretation.

The data set is all the data collected in a particular study.

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Elements are the entities on which data are collected.

A variable is a characteristic of interest for the elements.

An observation is the set of measurements obtained for a particular element.

Elements, Variables, and Observations

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NQ 73.10 0.86 N 74.00 1.67 N 365.70 0.86 NQ 111.40 0.33 N 17.60 0.13

Stock Annual Earn/Exchange Sales($M) Share($)

Data Sets, Elements, Variables, and Observations

Dataram EnergySouth Keystone LandCare Psychemedics

N 74.00 1.67

Variables

Elements

Data Set

Observation

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Scales of Measurement

Nominal

Ordinal

Interval

Ratio

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Scales of Measurement

Nominal – labels or names.• E.g., CoB, CoST, CoAL, CoH; male or female;

department 1, 2, 3, 4, … Ordinal - have the properties of nominal data

and the order or rank of the data is meaningful.• E.g., Freshman, Sophomore, Junior, or Senior

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Scales of Measurement

Interval – have the properties of ordinal data, and the interval between observations is expressed in terms of a fixed unit of measure.• E.g., ACT score of 23, 24, 25, …; years.• Numeric

Ratio - have all the properties of interval data and the ratio of two values is meaningful.• E.g., 30 credit hours versus 120 credit hours• Must include zero

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What You Can Do With Scales

Compute Nominal Ordinal Interval Ratio

Frequency distribution. Yes Yes Yes YesMedian and percentiles. No Yes Yes YesAdd or subtract. No No Yes YesMean, standard deviation, standard error of the mean.

No No Yes Yes

Ratio or coefficient of variation. No No No Yeshttp://www.graphpad.com/faq/viewfaq.cfm?faq=1089

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Categorical or Quantitative DataCategorical (or Qualitative) Grouped by categories Numeric or non-

numeric Nominal or ordinal

Quantitative How much or how

many Numeric Interval or ratio More statistical tests

available

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Scales of Measurement

Categorical Quantitative

Numeric NumericNon-numeric

Data

Nominal

Ordinal

Nominal Ordinal Interval Ratio

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Cross-Sectional or Time Series Data

Cross-sectional data are collected at the same or approximately the same point in time.• E.g., Building permits in January

Time series data are collected over several time periods.• E.g., Building permits each month

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Data Sources

Existing Sources – data already exists. Statistical Studies – data obtained through a

study.• Experimental Studies – variable of interest

identified and other variables controlled.• Observational studies – no attempt is made

to control or influence the variables of interest.

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Descriptive Statistics

Data summarized and presented in a form that is easy for the reader to understand.

Tabular, graphical, or numerical.

Average Tune-up= $79

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Statistical Inference

Use data from a sample to make estimates or test hypotheses about a population.

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Statistical Inference

Population – set of all elements in a particular study.• Census – collects data about entire

population. Sample – a subset of the population.

• Sample survey – collects data for a sample.

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Statistical Inference

Population Sample

Statistics about sample

Statistics about the sample provide an estimate of the population.

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