Introduction to Statistics by 7n2Mpe

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```									Introduction to Statistics
Intro. to Statistics
   What is Statistics?
• “…a set of procedures and rules…for
reducing large masses of data to
manageable proportions and for
allowing us to draw conclusions from
those data”
Intro. to Statistics
   What can Stats do?
• Make data more manageable
   Group of numbers:
6, 1, 8, 3, 5, 4, 9
   Average is: 36/7 = 5 1/7
   Graphs:
90
80
70
60
East
50
West
40
North
30
20
10
0
1st Qtr 2nd Qtr 3rd Qtr 4th Qtr
Intro. to Statistics
   What can Stats do?
• Allow us to draw conclusions from the data
   Variable = Coolness
   Group #1: 6, 1, 8, 3, 5, 4, 9
• People who take my stats class
• Average is 5 1/7
   Group #2: 8, 3, 4, 2, 7, 1, 4
• People who take other people’s stats classes
• Average is 4 ¼
   What can we conclude from these numbers?
• Allows us to do this objectively and
quantitatively
Intro. to Statistics
   “Quantitative”           “Qualitative”
• Involves                • Describes the
measurement               nature of
• Data in numerical         something
• Answers “How              “Of what kind”
much” questions           questions
• Objective and           • Often evaluative
results in                and ambiguous
unambiguous
conclusions
Intro. to Statistics
   Qualitative Distinctions:
• “Right” versus “Wrong”
• “A Lot” versus “A Little”
   Quantitative Distinctions:
• 5 1/7 versus 4 ¼
• 25% versus 50%
• 1 hour versus 24 hours
Basic Terminology
   Summarizing versus Analyzing
   Descriptive Statistics
   Inferential Statistics
• Inference from sample to population
• Inference from statistic to parameter
• Factors influencing the accuracy of a sample’s
ability to represent a population:
   Size
   Randomness
Basic Terminology
• Size –
   Sample of 5 cards from a deck of 52
• 2 of Clubs, 10 of Diamonds, Jack of Hearts, 5 of
Clubs, and 7 of Hearts
   What could we conclude about the full deck
from this sample about what the full deck
looks like without any prior knowledge of a
deck of cards?
   Compare this to a sample of 51/52 cards –
What could we conclude from this sample?
Basic Terminology
• Randomness –
   This time lets use the same 5 card sample,
but this time the deck is unshuffled
(nonrandom)
• 2 of Clubs, 10 of Clubs, Jack of Clubs, 5 of Clubs,
and 7 of Clubs
   What would we conclude about the
characteristics of our population (the deck)
this time versus when the sample was more
random (shuffled)?
Basic Terminology
   Most often, the aim of our research
is not to infer characteristics of a
population from our sample, but to
compare two samples
• I.e. To determine if a particular
treatment works, we compare two
groups or samples, one with the
treatment and one without
Basic Terminology
• We draw conclusions based on how similar the
two groups are
   If the treated and untreated groups are very similar,
we cannot declare the treatment much of a success
   Another way of putting this in terms of
samples and populations is determining if
our two groups/samples actually come
from the same population, or two different
ones
Basic Terminology
   Group A (Treated) and B (Untreated)
are sampled from different
populations/treatment worked:

Group A                     Group B
Population of Well People   Population of Sick People
Basic Terminology
   Group A and B are sampled from the
same population/treatment didn’t
work:

Group A
Group B
Population of Sick People
Basic Terminology
   Quantitative Data
• Dimensional/Measurement Data versus
Categorical/Frequency Count Data
   Dimensional
• When quantities of something are measured on a
continuum
• I.e. scores on a test, measures of weight, etc.
Basic Terminology
   Categorical
• When numbers of discrete entities have to be
counted
 Gender is an example of a discrete entity –

you can be either male or female, and nothing
else – speaking of “degree of maleness”
makes little sense
• I.e. number of men and women, percentage of
people with a given hair color
Basic Terminology
   A dimensional variable can be
converted into a categorical one
• Convert scores on a test (0-100) into
“Low”, “Medium”, and “High” groups –
0-33 = Low; 34-66 = Medium, and 67-
100 = High
   The groups are discrete categories (hence
“categorical”), and you would now count
how many people fall into each category

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