Statistics Types of Data https://www.123rf.com/photo_6622261_statistics-and-analysis-of-data-as-background.html

Types of Data In science (and statistics), evidence is called “data” (no… not that kind of “Data”) http://images2.fanpop.com/image/photos/9400000/Lt-Commander-Data-star-trek-the-next-generation-9406565-1694-2560.jpg

Types of Data Data! adquadrant.com

Science (and Statistics) deals only with things that are Types of Data Science (and Statistics) deals only with things that are Measurable Replicable undsci.berkeley.edu nationaldaycalendar.com

Types of Data Two levels of measurement for data: counts measurements nationaldaycalendar.com www.shutterstock.com

Types of Data Two classifications of data: qualitative – a category quantitative – a number Qualitative Quantitative

Types of Data We count qualitative data (how many fall into each category) We measure quantitative data

Types of Data IN-CLASS PROBLEMS Lengths of time three brands of aspirin take to cure headaches Counts or measurements? Qualitative or quantitative?

Types of Data IN-CLASS PROBLEMS Speed of your car taken by the cop Count or measurement? Qualitative or quantitative?

Types of Data IN-CLASS PROBLEMS Maximum daily temperatures for Denver 1880-2011 Counts or measurements? Qualitative or quantitative?

Types of Data Some numbers are really names! (qualitative, not quantitative)

Types of Data IN-CLASS PROBLEMS List of social security numbers Count or measurement? Qualitative or quantitative?

Types of Data IN-CLASS PROBLEMS Your CO driver’s license info Counts or measurements? Qualitative or quantitative?

Types of Data IN-CLASS PROBLEMS The “Q” Game

Questions?

Best Descriptor Traditionally, we split data into quantitative and qualitative types because this determines what statistical descriptors we will calculate to summarize our data and answer our questions

Best Descriptor You use a statistic (descriptive number) called the “mode” for qualitative (categorical) data

Best Descriptor You use a traditional average (arithmetic mean) for quantitative data

What type of data are these: Best Descriptor IN-CLASS PROBLEMS What type of data are these:

Best Descriptor IN-CLASS PROBLEMS What single value would you use for the “typical” response to this survey question:

The most commonly occurring response (the mode) is “brown” Best Descriptor IN-CLASS PROBLEMS The most commonly occurring response (the mode) is “brown”

What type of data are these: Best Descriptor IN-CLASS PROBLEMS What type of data are these:

Best Descriptor IN-CLASS PROBLEMS What single value would you use to illustrate the “typical” response to this experimental result:

For this, the “average” height of the 12 students would be better Best Descriptor IN-CLASS PROBLEMS For this, the “average” height of the 12 students would be better

Questions?

Measurement Scales or number systems used to measure something we want to know

Measurement four levels of scale measurement

Qualitative or quantitative? Measurement IN-CLASS PROBLEMS four levels of scale measurement Nominal - assigns a value to an object for identification or classification purposes only – a “name” Qualitative or quantitative?

Measurement four levels of scale measurement Nominal: What is your hair color? Represents unordered categories

Qualitative or quantitative? Measurement IN-CLASS PROBLEMS four levels of scale measurement Nominal Ordinal - things are arranged in order based on how much of some concept they possess – a “rank order” Qualitative or quantitative?

Measurement four levels of scale measurement Nominal Ordinal:  Disagree  Neutral  Agree an ordered scale of agreement

Qualitative or quantitative? Measurement IN-CLASS PROBLEMS four levels of scale measurement Nominal Ordinal Interval - capture information about differences in quantities Qualitative or quantitative?

Measurement four levels of scale measurement Nominal Ordinal Interval: Temperature! The difference between 32° and 42° is the same as between 400° and 410°

Qualitative or quantitative? Measurement IN-CLASS PROBLEMS four levels of scale measurement Nominal Ordinal Interval Ratio - represent absolute quantities – have a true zero Qualitative or quantitative?

Measurement four levels of scale measurement Nominal Ordinal Interval Ratio: Sam makes twice as much money as Pauline – and Gerry makes zero money!

Measurement True ratio-level data are found by measuring stuff with a piece of measurement equipment or a test of some sort

Questions?

It’s Not Black and White It is traditional to teach the levels of measurement in an introductory statistics class

It’s Not Black and White This is because the level of measurement theoretically determines the appropriate statistical analysis to be used

It’s Not Black and White In practice, it is not always clear cut

It’s Not Black and White We are CONSTANTLY changing measurement data to count data…

It’s Not Black and White …and count data are (because they are counts) used like measurements

It’s Not Black and White In practice, ordinal scales containing five or more categories of response are treated as interval When fewer than five categories are used, this is inappropriate

It’s Not Black and White The Likert Scale Likert scaling is bipolar - it measures either positive or negative response to a statement Rensis Likert (1903-1981)

It’s Not Black and White The format of a typical five-level Likert item:  Strongly disagree  Disagree  Neither agree nor disagree  Agree  Strongly agree

It’s Not Black and White Because Likert scale items typically have 5 or more categories, they can be treated as interval-level (you can calculate an “average” response

It’s Not Black and White IN-CLASS PROBLEMS What level of measurement are these data?

It’s Not Black and White IN-CLASS PROBLEMS What is the “usual” response for these items?

It’s Not Black and White A calculated weighted average for the responses: How would you rate your recycling frequency: Response Score Resp x Score all the time 4 5 20 frequently 13 52 often 15 3 45 sometimes 14 2 28 rarely 1 never 12 Sum 63 150 Average 2.380952

Questions?

Measurement Criteria Three Criteria for Good Measurement: reliability, validity and sensitivity

Measurement Criteria Reliability is an indicator of a measure’s internal consistency A measure is reliable when different attempts at measuring something converge on the same result

Measurement Criteria Is it consistent?

Measurement Criteria Validity is the accuracy of a measure or the extent to which a score truthfully represents a concept

Measurement Criteria Are we accurately measuring what we think we are measuring? Accurate Precise Accurate but not precise but not accurate and precise

Measurement Criteria Sensitivity is the ability to accurately measure the subtle variability in a concept

Measurement Criteria Which will measure subtle differences better:  agree  disagree or: strongly agree mildly agree neither agree nor disagree mildly disagree strongly disagree

Questions?