1Copyright Barbara Mitchell, MA, CSP, Cambria Cty Comm Coll

Spring 2004

Parsing* Peanut Butter

An investigation of data types in the behavioral sciences

*Parse: to analyze something in an orderly way.

featuring

Spring 2004 Copyright Barbara Mitchell, MA, CSP, Cambria Cty Comm Coll

page 2

Knowing About Data Types• Who cares? You do!

• Why?– Knowing the type of data helps you to judge the

validity (value??) of research• And therefore the amount of “trust” you can put in a claim

– Knowing the type of data allows you to choose the type of statistical analysis to conduct

Based on Graziano & Raulin, 2004, Allyn Bacon

Spring 2004 Copyright Barbara Mitchell, MA, CSP, Cambria Cty Comm Coll

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Let’s get started• There are

fundamentally two types of data– Categorical

– Continuous

Measurement (Score data)

Spring 2004 Copyright Barbara Mitchell, MA, CSP, Cambria Cty Comm Coll

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Categorical sorts data into categories or groups

• Nominal – where the order of the items

or objects is arbitrary (unordered)– For example: all colors of cats

• Ordinal– where there is a logical ordering to the items or

objects (ordered or ranked in a meaningful way)– For example: all shades of blue

Spring 2004 Copyright Barbara Mitchell, MA, CSP, Cambria Cty Comm Coll

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Nominal Datum (plural=Data)

• The only property of nominal data is IDENTITY• Nominal Scales are NAMING scales:

– Names of babies– Names of political parties

• Numbers may be assigned but they are meaningless, ex. Blue = 1 and red = 2 does not mean that blue is ½ of red

• Nominal Scales classify or categorize• Nominal data can only be understood in terms of the

frequency of occurrence• Chi Square is the most common statistical test for

nominal data

Spring 2004 Copyright Barbara Mitchell, MA, CSP, Cambria Cty Comm Coll

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Test yourself• Nominal or Ordinal

– Learning style – Non-smoker– Peanut butter taste (good, bad)– Freshman, sophomore, junior, senior– Peanut butter taste (pleasant, less than

pleasant, indifferent, a little odd, unpleasant

Nominal

Nominal

Nominal

Ordinal

Ordinal

Not so good-Go Back Did OK – Move On

Spring 2004 Copyright Barbara Mitchell, MA, CSP, Cambria Cty Comm Coll

page 7

Another Test

• Data on juice preferences

• Data on Shreck likeability

• Data on myth gullibility

• Data on illness severity

• Number of students getting an “A”

• Crayon color (red blue, green)

Ordinal

Ordinal

Ordinal

Ordinal

Nominal

Nominal

Spring 2004 Copyright Barbara Mitchell, MA, CSP, Cambria Cty Comm Coll

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So What’s with the Peanut Butter?

• You can collect Nominal data

• You can collect Ordinal data

Do you like Peanut Butter? (YES or NO)

How much different is brand X from brand Y?

Spring 2004 Copyright Barbara Mitchell, MA, CSP, Cambria Cty Comm Coll

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Nominal Data• IS

– Unordered– Objects cannot be put

in a logical (increasing or decreasing) sequence

– There is no better or worse– Often found in a

YES/NO (more/less) format

Spring 2004 Copyright Barbara Mitchell, MA, CSP, Cambria Cty Comm Coll

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Statistical Evaluation of Nominal Data• Since you cannot mathematically operate on

YES /NO type questions…• And you have the problem that there is no

MAGNITUDE between any two items, by definition, cannot be the same…

• Your analytical choices are– Frequency distributions, percentages– Chi-square(Χ2) goodness of fit, and (Χ2) test for

independence

Spring 2004 Copyright Barbara Mitchell, MA, CSP, Cambria Cty Comm Coll

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Ordinal Data• IS

– In some sort of logical order

– Each relates to the other in some way

– May indicate a preference or value, asks HOW MUCH? But is not ‘measurable’

– Most often seen in a “Likert” scale• “totally agree’ |‘agree’ | ‘no preference’ | ‘disagree’ | ‘totally

disagree’

In 1932, Renis Likert invented a measurement method, called the Likert Scales, used in attitude surveys. They allowed answers that ranged from "strongly disagree" to "strongly agree."

Retrieved 3.14.04 from www.nwlink.com/~donclark/hrd/history/likert.html

Spring 2004 Copyright Barbara Mitchell, MA, CSP, Cambria Cty Comm Coll

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Ordinal Data Properties• Have IDENTITY and MAGNITUDE as properties• Numbers represent an order of some sort• City size (sq. miles, or # of people), class rank,

grades of ABCDF are ordinal data.• Ordinal data CANNOT be compared because

there is no information about the differences between categories or ranks

• For example – a LIKERT SCALE of |The Best!| Nice| OK| So-So| Uck!|Tells us nothing about the DISTANCE between each choice. There is no way to measure relative size.

Spring 2004 Copyright Barbara Mitchell, MA, CSP, Cambria Cty Comm Coll

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Statistical Evaluation of Ordinal Data

• Ordered (ordinal) data indicated that there is a relationship between the elements in the group.

• A Median can be located in an ordinal grouping to measure central tendency,

• A Range or Inter-quartile range can be calculated for variability,

• If describing a relationship in the data, then a Spearman rank-order correlation between the items can be calculated.

Ways to DESCRIBE the data

Spring 2004 Copyright Barbara Mitchell, MA, CSP, Cambria Cty Comm Coll

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Statistical Evaluation of Ordinal Data 2

• If you have 2 groups (IV1, IV2), and – The groups are independent, then the Mann-Whitney U-

test is used– The groups are not independent, the the Wilcoxon

signed-rank test is used

• If more than 2 groups, and– The groups are independent, then Kruskal-Wallis one-

way ANOVA– The groups are not independent, the Friedman 2-way

ANOVA (see p.325 in Graziano & Raulin, 2004)

Ways to make INFERENCES about the data

Spring 2004 Copyright Barbara Mitchell, MA, CSP, Cambria Cty Comm Coll

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Quiz Time

• Take the Quiz on Course Compass (Categorical Quiz)

If you did well, link to Part 2

If you need to see this section again

Spring 2004 Copyright Barbara Mitchell, MA, CSP, Cambria Cty Comm Coll

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Part 2a – Score Data (continuous) • Interval and Ratio data is continuous

with equal intervals between points…….– Have equal intervals between each measure,– That is, the distance (depth, temperature, amount)

from one point to the next (say point 1 to point 2) is the same as the interval between any other two consecutive points (so it would be the same from point 30 to point 31)

– All interval and ratio data can be operated on mathematically (add, subtract, multiply, divide, square root)*

• Ratio data has a meaningful ZERO pointOur book states that you can only add and subtract with interval data, however, others argue that you can conduct all five operations on interval data. Ratios can only be calculated on ratio data

Spring 2004 Copyright Barbara Mitchell, MA, CSP, Cambria Cty Comm Coll

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Part 2b – Interval Data Properties• Interval data have the properties if IDENTITY,

MAGNITUDE, and EQUAL INTERVALS between values on the scale- They ask HOW MUCH?

• Interval:– Fahrenheit & Centigrade (Zero is a reference

point)– Calendar Years– I.Q.– Family Income

• Note about I.Q. type tests: We CAN say that a score of 120 points is 60 points higher than a score of 60 points. But we CANNOT say that the one person is twice a smart as the other because there is NO TRUE ZERO

Spring 2004 Copyright Barbara Mitchell, MA, CSP, Cambria Cty Comm Coll

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Interval Statistical Properties

• Interval data cane be ADDED and SUBTRACTED.

• The Students t-test and the

• Analysis of Variance (ANOVA) are statistical tests that respect the limits if INTERVAL data

Spring 2004 Copyright Barbara Mitchell, MA, CSP, Cambria Cty Comm Coll

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Part 2c – Ratio Data Properties

• Ratio data has the properties of IDENTITY, MAGNITUDE, EQUAL INTERVAL, and a TRUE ZERO.

• Ratio– Kelvin (absolute Zero)– Years of Experience– Length– Age– Reaction times

Spring 2004 Copyright Barbara Mitchell, MA, CSP, Cambria Cty Comm Coll

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Ratio Statistical Tests

• The Students t-test and the

• Analysis of Variance (ANOVA) are statistical tests

• Product moment correlational tests, many others.

• Ratio/proportional data

Spring 2004 Copyright Barbara Mitchell, MA, CSP, Cambria Cty Comm Coll

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Test yourself• Interval or Ratio Data

– Response time to a customer – Smoking Reduction Program– Score on the SAT– Effects of medication training program– Improving speed of response

Interval

Interval

Ratio

Interval

Interval

Not so good-Go Back Did OK – Move On

Spring 2004 Copyright Barbara Mitchell, MA, CSP, Cambria Cty Comm Coll

page 22

Another Test

• Sugar concentration in Peanut Butter• Variation of Volume on Shrek Movie and

viewer complaints• Fat content of Peanut Butter & salivation• Data on childhood temperature ranges• SAT score of 560• Crayon quality as a % of wax

Ratio

Ratio

Interval

Interval

Ratio

Ratio

Spring 2004 Copyright Barbara Mitchell, MA, CSP, Cambria Cty Comm Coll

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More about Peanut Butter?• Interval Scale:

– Measuring sugar concentration in the mouth following eating of several different brands of peanut butter

• Ratio Scale– Measuring fat concentrations of peanut

butter relative to the amount of liquid drunk following the ingestion of 2 tablespoons of peanut butter.

Spring 2004 Copyright Barbara Mitchell, MA, CSP, Cambria Cty Comm Coll

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Statistical Tests for Interval and Ratio Data• Descriptive:

– Mean– Median– Mode

• Variability– Variance– Standard Deviation

• Related Groups: – Pearson product-moment

correlation

•Inferential:–T-test–ANOVA

See pp. 323 & 324 in Graziano & Raulin, 2004

Spring 2004 Copyright Barbara Mitchell, MA, CSP, Cambria Cty Comm Coll

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Quiz Time

• Take the Quiz on Course Compass (Score Quiz)

If you did well, link

If you need to see Section 2 again

Spring 2004 Copyright Barbara Mitchell, MA, CSP, Cambria Cty Comm Coll

page 26

PaRtY!

• By, George, I think you’ve gOt iT!