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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
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