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Kinds of Statistics

There are two broad categories of statistics. They are descriptive and inferentialstatistics and are depicted in the following image.

Descriptive statistics summarize population data numerically or graphically byderiving

o statistics pertaining to central tendency such as the mean, median, ormode

o statistics pertaining to dispersion around the central tendency such as therange or standard deviation

o statistics or graphs depicting the shape of a distribution

Inferential statistics allow one to infer population parameters based upon samplestatistics and to model relationships within the data. The categories of inferentialstatistics are

o Estimation is the group of statistics which allow for the estimation aboutpopulation values based upon sample data. The two types of statistics inthis category are population parameter estimates and confidenceintervals.

o Modeling allows us to develop mathematical equations which describe theinterrelationships between two or more variables.

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o Hypothesis testing allows us to test for whether a particular hypothesisweve developed is supported by a systematic analysis of the data.

Data Types and Measures

Developing a good understanding of the kinds of data and data measurement isnecessary because the kind of data you are analyzing essentially dictates the type ofstatistical analysis you perform. Data can be classified as either numerical(quantitative) or categorical (qualitative) and is presented below

Categorical data is data that can be sorted according to a category and eachvalue is from a set of non-overlapping values. Examples of categorical datawould include eye color (green, brown, blue, etc.) and managerial level(supervisor, mid-level, executive).

o Categorical variables are typically measured on a nominal scale.Nominal level variables are those that can simply be grouped; theres nounderlying numeric order to them and any ordering is arbitrary or artificial.Our examples above of eye color and managerial level are both measured

at a nominal level. Other examples of categorical data thats measured ona nominal scale include type of industry, state of residence, marital status,and favorite food. Please note that you might have responses dummy-coded with numbers to represent a response such as 0s representingmale and 1s representing female, but even though there are numbers itsstill a nominal scale because the ordering is completely arbitrary; we couldhave had 0s representing female and 1s representing male.

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Numerical data is data that is on a numerical scale of some sort.

o Discrete data is typically when theres a limited number of responsevalues and not an infinite number of response values. For exampleresponses on a five-point scale can be any of the five values but cannot

be 3.1 or 3.6 or 4.2, etc.

o Continuous data is when the response can take on any value within therange of variable. For example responses to the question of whats yourGPA on a 4.0 scale? could take on not just 1, 2, 3, or 4 but also 3.17,3.83, 2.94, etc.

o Numerical data is measured on an ordinal, interval, or ratioscale.

An ordinal scale is a measure where higher numbers do representmore of a characteristic than a lower level number but the distance

between adjacent response choices may not be equal and theresno fixed zero.

An interval scale, like an ordinal scale, is where higher numbersrepresent more or a greater amount of the phenomena beingmeasure, and where the distance between adjacent responsechoices are equal but theres still no fixed and non-arbitrary zero.Temperature, in Celsius or Fahrenheit, is the typical example of aninterval scale in which the distance between 5 and 6 is the same asthe distance between -22 and -21 and is the same as the distancebetween 102 and 103. But, it doesnt make sense to say that 50 is

twice as hot as 25 because 0 degrees, for both scales, is arbitrary.

A ratio scale has the same properties as an interval scale, exceptthat there is a true zero and calculating ratios makes sense. Forexample, to say that someone has twice the income of anotherperson is correct, at least mathematically. Sales for a particularretailer can be compared with ratios or percentages from same timelast year, etc.

Measurement scales are depicted graphically below.

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Now, think about how people would respond to the following questions. What type ofdata and measurement scale would each of the following represent?

What is your favorite sport?

Do you like opera?

How many hours per week do you watch television?

What kind of music do you like?

To what degree do you enjoy reading novels?

On a scale of from 1 (Dislike) to 7 (Like), how much do you like Italian food?

In what state were you born?

What do you think, in terms of percentage of income, is acceptable for a single

individual who has no dependents and earns $250,000 per year to pay in federalincome tax?