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Sociology

SOC202H1

Mitch Mc Ivor

Winter

Description

AN INTRODUCTION TO STATISTICS FOR CANADIAN
∑ (x−x) 2 | x− x |
s = ∑ N
N
SOCIAL SCIENTISTS—MICHAEL HAAN
CH 1. WHY SHOULD I WANT TO LEARN STATISTICS?
• Probabilities
• Sampling Error
CH 2. HOW MUCH MATH DO I NEED TO LEARN STATISTICS?
• Order of operations—BEDMAS
(1) # Of hours at the mall= 0.2 x # of Friends + (0.01 x disposable income – 4
x Age) –0.2 x # of Security guards at mall +2
(2) Y=aχ+b
(3) 0.2 x 3 (0.01 x 10,000—20x4) –0.2 x 25+2
(4) 0.6 + (100—80) –5 + 2
(5) 0.6 + 20 –3=17.6 Hours/ Month
• Exponents— 2 =4
• Logarithm—log1000 = 3 or log 1000 = 3: logarithm is a way of stating
that when 10 is the base it must be multiplied by itself 3 times (10 ) to
obtain the product of 1,000
LEVELS OF
MEASUREME Description Example
NT
Nominal Numbers are only the name of How many marathon
things. No level or order of runners are from each
significance country?
Ordinal Data can be placed into an order. Who came first, second,
Ranked –i.e. likert, but can not third place in the
measure level of significance marathon?
between ranks
Interval Can be in order, added or subtractedOn a scale from 1 (very
but not multiplied or divided unhappy) to 5 (very
happy), how did each
competitor feel as they
crossed the finish line?
Ratio Has meaningful “0” value and allows How much time did it for the exact difference between take to cross the finish
observations to be measured line?
CH 3. UNIVARIATE STATISTICS
• Frequencies tell us the number of times an item, or a response category
comes up in a sample
• i.e.) Number of Males and Females in Canadian Population, 2006 Census
of Canada
Sex (χ) Frequency % Cumulative Cumulative
Frequency %
F 16,136,930 51.05 16,136,930 51.05
M 15,475,970 48.95 31,612,895 100.00
• Bar Charts
o Response categories must always appear on the χ-axis | frequency
should always be on the y-axis
• Pie Chart
o Legends, titles, data sources
• Ratios
o The number of observations in one category compared to the
number of observations in another category.
1. I.e. 16,136,930 F for every 15, 475, 970 M in Canada
2. To simplify it divide #’s by 100,000= 161:155
• Rates
o Rates usually used to present continuous data.
o Use the same denominator
Rates, Ratios, % are STANDARDIZED… use the same unit of measurement
CH 4. INTRODUCTION TO PROBABILITY
• Probability is a number between 0 and 1
o 0= Event NEVER occurs
o 1=Event OCCURS
• Sample Space All Possible Outcomes
o Contains all of the theoretically possible outcomes of an event
o Each probability is a fraction of All Possible Outcomes
• Law of Large Numbers
o States that if you repeat a random experiment, many, MANY
times… your outcome will reach a level of stability—meaning it will
come out as the theoretical probability
• Theoretical probability
o What is predicted to occur
• Empirical Probability o Trials conducted to see if it occurs
• Mutually Exclusive
o Does not overlap, and are independent outcomes
• Not Mutually Exclusive
o When an outcome of a probability that occurs OVERLAPS, you
must subtract its duplicate
o I.e.) Draw out a king or a heart from a deck of cards= 4/25 +13/25
-1/25=
• Probability of Unrelated Events
o Independent—event that occurs is independent
• Probability of Related Events
o Dependent—when the event that occurs is dependent on an event
that occurred prior. I.e.) 1 bullet in 6 rounds, person A shoots a
blank, therefore your chances turn to 1/5
• Mutually Exclusive Probabilities That are Interchangeable
o I.e. What is the probability of rolling a die and yielding EITHER 1 or
6
ONE= 1/6
SIX=1/6
ONE or SIX = 1/6 + 1/6= 2/61/3
• Non-Mutually Exclusive or Interchangeable probabilities
o When two events can occur simultaneously –considered to be non-
mutually exclusive
o Overlap, therefore subtract the duplicate
CH 5. THE NORMAL CURVE
• Central Limit Theorem—same as Law Of Large Number, except CLT
applies to graphs not just outcomes
• ASYMPTOTIC means that the central limit theorem will exist—the more
you run a trial to test it, the more “normal” it will become
• Unimodal—One hump (Mode—the most frequently occurring value in
data set, on a variable of interest)
• Bimodal—two modes i.e. gender (F and M)
• Multimodal- multiple modes
• SKEW vs. SYMMETRICAL (normal bell curve) CH 6. MEASURES OF CENTRAL TENDENCY
• MEAN: Average i.e. Grade calculation
• MEDIAN: The value in the middle
• MODE: The most frequently occurring value
• RANGE = Highest Value- Lowest Value
o Used to see how wide or spread out the values are
o I.e. 5 year income values—$25,000 - $5,000 = $20,000
• MEAN DEVIATION
o Can tell you how far someone is from the average value—the
average distance
o MEAN DEVIATION=
o Translation: the sum of |the values of the observation-
mean/average| all divided by total number of values
o Steps to calculate:
1. Calculate the average
2. Subtract each value from the mean/average
3. Sum the absolute values (make values positive)
4. Divide the sum by the total number of observations
I.e. Average is 70, student A gets 60, Student B gets 80
Student A’s mean deviation =10, Student B’s mean
deviation =10,
• VARIANCE AND STANDARD DEVIATION o Like the mean deviation, the variance and standard deviation
are measures of how far the average observation is from the
mean
o BUT… that variance and standard deviation maintain the
integrity of the data by transforming all of the data versus
just some of it.
2
2 ∑ (x−x)
o s = N ▯
o Steps to calculate Variance:
1. Calculate the average
2. Subtract the mean/average from each value
3. Squaring the differences! ( )
4. Add the squared deviations together
5. Divide the sum by the number of observations
NOW… simply just square root of the results to end up with
standard deviation!
CH 7. STANDARD DEVIATIONS, STANDARD SCORES, & THE NORMAL
DISTRIBUTION
• What would the law of large numbers look like if it were drawn out?
• How to compare the values of different groups within a sample
o Z-score
• The continuum is the normal curve
• Standard deviation and standard score are used to determine the
rank of an observation—Standard deviation is like money (units of
measurement)—always possible to compare 2 observations to each other
by using standard deviation scores
• Using the mean and S.D., the normal curve provides info about the
characteristics of a variable
• The mean provides a useful “cut-point” for assessing how a person ranks
—i.e. exam scores, are you above or below the average?
• μ = mu (Mean)—value of zero
• 68-95-99 • Knowing the SD allows us to est. the proportion of all hours where the
values are above and/or below the grand sample mean—we can also
determine the distance a particular observation is from the mean
•

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