Why is this important?

• Requirement

• Understand research articles

• Do research for yourself

• Real world

• Develops your analytical and critical thinking

Statistics

DescriptiveStatistics

Statistics

D esc rip tiveS ta tis t ic s

In fe ren tia lS ta tis t ic s

S ta tis t ic s

Practice

• Based on a sample of participants, it appears that a new drug will be effective at stopping headaches

• The enrollment in this course as of August 15th was 22

Practice

• On your first test you received a score of 84 out of 100

• Markey will likely be the next president; of the 100 people surveyed 82% said they would vote for him

Inferential Statistics

• Problem: Is that going to be the exact answer?

• Chance influences the sample– “true” variation– “error” variation

• Sample = “true” + “error”

Basic Terms

• Population – Consists of all the scores of some group

• Sample– Is a subset of a population

Basic Terms

• Parameters– A numerical or nominal characteristic of a

population

• Statistics– A numerical or nominal characteristic of a

sample

• Statistics change from one sample to the next -- Parameters are constant!!

Basic Terms

• Variable– Something that exists at more than one

amount

• Quantitative Variable– A score attached to a variable -- tells you

something about its amount

Quantitative Variable

148 149 150 151 152

148.5 149.5 150.5 151.5

Quantitative Variable

148 149 150 151 152

148.5 149.5 150.5 151.5

149.5 to 150.5

Quantitative Variable

50 51 52 53 54

50.5 51.5 52.5 53.5

Quantitative Variable

51.5 to 52.5

50 51 52 53 54

50.5 51.5 52.5 53.5

Quantitative Variable

48.4 48.5 48.6 48.7 48.8

48.45 48.55 48.65 48.75

Quantitative Variable

48.55 to 48.65

48.4 48.5 48.6 48.7 48.8

48.45 48.55 48.65 48.75

Quantitative Variable

• To find lower limit score:

– Subtract half the unit of measurement from the score

For 48.6 the unit of measurement is 0.1Half of 0.1 is 0.0548.6 - 0.05 = 48.55

Quantitative Variable

• To find upper limit score:

– Add half the unit of measurement from the score

For 48.6 the unit of measurement is 0.1

48.6 + 0.05 = 48.65

Qualitative Variable

• Are not continuous like quantitative variables

• They are usually words or names– e.g., gender, political party, religion

Practice

• 14, average number of minutes before a student falls asleep

• 4000, this course number

• 3.5, a students GPA

Practice

• 555-8904, Ned Flanders phone number

• 1,301, the average weight of the human brain in grams

Sample Cookbook Page

To find a quantitative numbers upper and lower limits

1) Determine the unit of measurement

Example: 14 = 1

14.2 = .1

14.29 = .01

Sample Cookbook Page

2) Calculate half the unit of measurement

Example: 1 = .5

.1 = .05

.01 = .005

Sample Cookbook Page

3) To find upper limit add half the unit of measurement to the original number

4) To find lower limit subtract half the unit of measurement to the original number

Sample Cookbook Page

Examples:

12 = 11. 5 to 12.5

12.3 = 12.25 to 12.35

12.34 = 12.335 to 12.345

The meaning of numbers

90

• The number correct on a test out of 100

• The last two digits of your SSN

• The percentile you scored on the SAT

Nominal Scale

• Are not really scales at all

• They do not scale items along any dimension, but rather label them

• Numbers are used as names and have no quantitative value

Nominal Scales

• Gender

• Political party

• Your SSN

• Religion

Ordinal Scales

• Has the characteristics of the nominal scale

• PLUS: the characteristic of indicating greater than or less than– i.e., RANK ORDER

Ordinal Scales

• Rank of professor

• Your place in a foot race

• Saying “This class is smaller then my other class”

Interval Scales

• Has the properties of BOTH the nominal and ordinal scales

• PLUS: the intervals between the numbers are equal– e.g., the distance between 4 and 5 is the

same distance between 1 and 2

Interval Scales

• Temperature– the difference between 10o F and 20o F is the

same as the difference between 80o F and 90o F

• Problem: What does 0o F mean?

• With interval scales you CAN NOT make ratio statements

Interval Scale

0 20 40 60 80

10 30 50 70

Appears twice as large

Interval Scale

-20 0 20 40 60

-10 10 30 50

Now it appears three-times as large!

Ratio Scales

• Has all the characteristics of the nominal, ordinal, and intervals scales

• PLUS: it has a true zero point

• This zero point indicates a complete absence of the thing measured

Ratio

• Weight

• Height

• Speed

• Distance

Features of the four scales

QuantitativeVariation

EqualIntervals

Zero Point

Ratio YES YES YES

Interval YES YES NO

Ordinal YES NO NO

Nominal NO NO NO

Why are the types of scales important?

• They help you understand what type of statistic to use

Practice

• Inches on a yardstick

• Drivers licenses number

• Dollars as a measure of income

• Order of finish in a car race

• Intelligence test scores