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Sociology

SOC222H5

John Kervin

Winter

Description

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SOC 222 -- MEASURING the SOCIAL WORLD
Session #5 -- INTRO to INFERENTIAL STATISTICS
SPSS: E Notation
When numbers are very small
SPSS converts to E notation
EG: 1.34E-2 = .0134
• 1.34 is the starting number
• E means move the decimal point
• minus sign – move to the left (negative direction)
• 2 is number of spaces to move the decimal point
EG: 7.89E-3 = .00789
• If no minus sign, or a plus sign, move decimal point to the right
EG: 1.34E+4 = 13400
- Write original and then use ^ method to indicate what to do with the decimal
- Test: just round before hand and then write it in.
POPULATIONS & SAMPLES
Effects size: was the first question we were assessing
Q2: if we use a sample how good is the estimate for the population.
Inferential because we infer something based on sample data
1. Population:
- A population is a group cases were interested in.
- We have a research question regarding that group
2. Sample:
- Set of cases selected form the population 2
3. Simple random sample
• random sample
1. set of cases selected from the population
2.
• simple random sample: each case has the same probability of
being chosen (SRS)
cases are selected by change
each case in the population has a known probability of being
selected
• statistic
- What we calculate from the sample is the statistic. Sample of students: statistic
would be mean age. Case would be one student
- Mean, correlation are all statistics calculated from the sample
• population characteristic
- we estimate population characteristics based on statistics
• population value
• parameter
SAMPLES & POPULATION ESTIMATES
• The sample effect size is our estimate of the effect size in the population.
- We don’t have time to obtain data from the entire population, thus we draw a
sample.
- The sample is the source of our data, and then we use that sample data to get a
statistic.
ACCURACY of ESTIMATES
- We cannot be sure that the sample characteristic is the same and represents the
entire population
- Drawing a second population sample and getting different results will not be a
surprise
- No sample is 100% accurate
Rick Example
- Why is the sample inaccurate? 3
• This is his RQ: what is the mean days absent for company employees?
• He can only afford a certain number from the population.
• We know what rick does not; what the population is.
Rick knows:
• The company has six employees
• He also knows that he can get info on employee from the personal department
w/o interviewing employee.
Here’s what Rick doesn’t know: (the population data):
Employee Days Absent
Ann 1
Bob 3
Cathy 3
Donna 5
Ed 7
Farrah 9
∑ xi 1+3+3+5+7+9 28
x= = = =4.67
N 6 6
Estimating a Population Mean from a Sample
• Cathy and Farrah
- Rick can only get data from 2 people, so he picks these two randomly.
- Next he finds that cathy was absent 3 days and farah was absent 9 days
- He concludes sample mean is 6
Summary:
• The sample mean is 6.0 days absent, on average
• So Rick’s estimate of the population mean is 6.0 days
• The true population mean is 4.67
• So Rick’s estimate is inaccurate by 1.33 days.
GOOD AND BAD SAMPLES
- How accurate is my estimate of 6 days ^.
- We know that his estimate is quite off
- Why does a sample give an inaccurate sample:
o Because you might get a sample that gives a good or maybe a poor
estimate. It depends on what sample you draw 4
Employee Days Absent
Ann 1
Bob 3
Cathy 3
Donna 5
Ed 7
Farrah 9
15 possible samples of size two
- How many sample of size two can we get from population. There are 15 possible
samples.
• The fourth column is the sample accuracy:
• Arbitrary:
• High: estimate is off by 1 day or less
• Means of 4 or 5
• This is a good sample
• Low: estimate is off by 2 days or more
• Means of 2 or 7 or 8
• Low accuracy sample
Sample Days Absent Sample Mean Sample
Accuracy
A, B 1, 3 2.0 Low
A, C 1, 3 2.0 Low
A, D 1, 5 3.0
A, E 1, 7 4.0 High
A, F 1, 9 5.0 High
B, C 3, 3 3.0
B, D 3, 5 4.0 High
B, E 3, 7 5.0 High
B, F 3, 9 6.0
C, D 3, 5 4.0 High
C, E 3, 7 5.0 High
C, F 3, 9 6.0
D, E 5, 7 6.0
D, F 5, 9 7.0 Low
E, F 7, 9 8.0 Low
Employee Days Absent
Ann 1 5
Bob 3
Cathy 3
Donna 5
Ed 7
Farrah 9
Representative sample: A sample with a distribution that matches the population
distribution.
Employee Days Absent
Ann 1
Bob 3
Cathy 3
Donna 5
Ed 7
Farrah 9
• 6 samples give good estimates
• 5 are so-so
• 4 are bad
The quality of the estimate depends on whether the sample is representative
Sampling Error
Sampling error: the probability of drawing a sample that gives an inaccurate
population estimate.
- There is always a chance that the sample you draw will not be
representative.
Rick’s Probability of a Bad Sample
In the Rick example:
• 15 possible samples
• 4 were bad
• So probability of drawing a bad sample is 4/15
• = 27%
• This is the sampling error for Rick’s sample
- Rick does not know the means of all the samples, so he cannot calculate the
probability of drawing a bad sample (sampling error) 6
Estimating Sampling Error
- If rick can estimate a sampling error, then he can know if the chance of drawing a
bad sample is high, then he might have drawn a bad sample. But if he knows that
the chance of drawing a bad sample is low, then he mostly likely does not have a
bad sample.
- So if we know that the chance is high to get a bad sample, then we might have
drawn a bad one so we

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