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ATS2946: Critical Thinking
创建日期：2024-06-05 15:38:11
所属分类：统计学statistics
标签： ATS2946
Critical Thinking

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1.Generalizations & Inductive Inferences 2.Sample Size 3.Sample Biases 4.Conclusion

ATS2946: Critical Thinking
Week 7: Inference from a Sample
1.Generalizations & Inductive Inferences 2.Sample Size 3.Sample Biases 4.Conclusion
Generalizations & Inductive Inferences
Arguments often include generalizations among their premises.
These can be:
‚ Universal Generalizations: All emeralds are green
‚ Statistical Generalizations: 90% of people are right-handed.
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1.Generalizations & Inductive Inferences 2.Sample Size 3.Sample Biases 4.Conclusion
Generalizations & Inductive Inferences
Generalizations typically concern a ‘population’ i.e. a set of things.
E.g.
All emeralds are green; population “ emeralds.
90% of people are right-handed; population “ people.
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1.Generalizations & Inductive Inferences 2.Sample Size 3.Sample Biases 4.Conclusion
Generalizations & Inductive Inferences
Generalizations invoke a ‘target property’ i.e. a feature that some mem-
bers of the population might have.
E.g.
All emeralds are green; target property “ greenness.
90% of people are right-handed; target property “ right-handedness.
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1.Generalizations & Inductive Inferences 2.Sample Size 3.Sample Biases 4.Conclusion
Generalizations & Inductive Inferences
Populations we want to generalize about are often too big to inspect every
member for the target property.
So we check a sample & make an inductive about the population.
Sample “ the members of the population actually examined.
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1.Generalizations & Inductive Inferences 2.Sample Size 3.Sample Biases 4.Conclusion
Generalizations & Inductive Inferences
The inductive inference looks like this:
P1. 90% of people in the sample are right-handed.
The sample is representative of the population as a whole.
Therefore,
C. 90% of all people are right-handed.
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1.Generalizations & Inductive Inferences 2.Sample Size 3.Sample Biases 4.Conclusion
Generalizations & Inductive Inferences
The inductive inference looks like this:
P1. 90% of people in the sample are right-handed.
A1. The sample is representative of the population as a whole.
Therefore,
C. 90% of all people are right-handed.
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1.Generalizations & Inductive Inferences 2.Sample Size 3.Sample Biases 4.Conclusion
Generalizations & Inductive Inferences
In general:
P1. x% of As in the sample are B.
A1 The sample is representative of the population of As as a whole.
Therefore,
C. x% of all As are B.
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1.Generalizations & Inductive Inferences 2.Sample Size 3.Sample Biases 4.Conclusion
Generalizations & Inductive Inferences
Extreme cases might include:
P1. 100% of As in the sample are B.
A1 The sample is representative of the population of As as a whole.
Therefore,
C. All As are B.
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1.Generalizations & Inductive Inferences 2.Sample Size 3.Sample Biases 4.Conclusion
Generalizations & Inductive Inferences
Extreme cases might include:
P1. 0% of As in the sample are B.
A1 The sample is representative of the population of As as a whole.
Therefore,
C. No As are B.
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1.Generalizations & Inductive Inferences 2.Sample Size 3.Sample Biases 4.Conclusion
Generalizations & Inductive Inferences
A sample that’s not representative of the population is said to be biased.
There are numerous reasons a sample can be biased.
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1.Generalizations & Inductive Inferences 2.Sample Size 3.Sample Biases 4.Conclusion
Sample Size
Small samples are liable to be biased.
Sometimes samples are so small they’re guaranteed to be biased.
Suppose you ask a sample of 1 person whether they’re left-/right-handed.
Either 0% or 100% of your sample is right-handed.
This deviates from the population figure of 90%.
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1.Generalizations & Inductive Inferences 2.Sample Size 3.Sample Biases 4.Conclusion
Sample Size
In a sample of 2 the possibilities are 0/2 (0%), 1/2 (50%), 2/2 (100%).
In a sample of 3: 0/3 (0%), 1/3 (33%), 2/3 (66%), 3/3 (100%).
Etc.
With these small samples we’re guaranteed figures that deviate quite sig-
nificantly from the population figure of 90%.
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1.Generalizations & Inductive Inferences 2.Sample Size 3.Sample Biases 4.Conclusion
Sample Size
Even in bigger samples it’s not guaranteed we’ll get figures representative
of population-level statistics.
In a sample of 10 people it’s possible that exactly 9/10 are right-handed.
But the chance of this is less than 40%.
This gives us a ą 60% chance that our figure is out by at least 10 per-
centage points!
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1.Generalizations & Inductive Inferences 2.Sample Size 3.Sample Biases 4.Conclusion
Sample Size
Even in a sample of 100, 1000, or 1000000 it’s not guaranteed that we’ll
get a figure of precisely 90%.
Indeed it’s unlikely we’ll get precisely 90/100, 900/1000, or 900000/1000000.
However, the larger the sample the more likely it is that the % in the
sample will be very close to the % in the population.
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1.Generalizations & Inductive Inferences 2.Sample Size 3.Sample Biases 4.Conclusion
Sample Size
Sample size more important than proportion of the population sampled.
Suppose we have some well-mixed marbles, 50% red & 50% blue.
We can either use a spoon that picks 4 marbles or a scoop that picks 100.
Far more chance our sample contains a % of red marbles close to 50 if we
use the big scoop than the spoon.
This affects our chance of getting a representative sample far more than
the size of the population as a whole: bathtub vs. swimming pool vs.
whole ocean of marbles.
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1.Generalizations & Inductive Inferences 2.Sample Size 3.Sample Biases 4.Conclusion
Sample Bias
Sample size is important but it doesn’t guarantee representativeness!
Even very large samples can generate unrepresentative results if they are
selected or tested in the wrong way.
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1.Generalizations & Inductive Inferences 2.Sample Size 3.Sample Biases 4.Conclusion
Sample Bias
Most types of sample bias fall into two categories:
1. Selection Bias: The way members of the sample are selected for
inspection/testing is liable to lead to a non-representative sample.
2. Measurement Bias: The way members of the sample are inspected/texted
leads to non-representative findings.
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1.Generalizations & Inductive Inferences 2.Sample Size 3.Sample Biases 4.Conclusion
Sample Bias
1. Selection Bias: The way members of the sample are selected for
inspection/testing is liable to lead to a non-representative sample.
E.g. We might suppose most of our prehistoric ancestors lived in caves.
After all caves are where we find most evidence (paintings, etc.).
Suppose:
Population = all prehistoric peoples
Sample = those whose behavior we have empirical evidence about
Our sample is likely heavily biased because the dwellings and activities
of any who didn’t live in caves are far more likely not to have been well
preserved. (‘The Caveman Effect’)
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1.Generalizations & Inductive Inferences 2.Sample Size 3.Sample Biases 4.Conclusion
Sample Bias
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1.Generalizations & Inductive Inferences 2.Sample Size 3.Sample Biases 4.Conclusion
Sample Bias
Self-selection can also lead to selection biases.
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MOEC0021 STA 106 ENGG 1300A ENGG 1300 OLET1139 STAT 3503 STAT 206 FEM11149 ELEN 4720 COMP20003 SOLA1070 CS574 C11CS LINB29H3 MAST90083 ECON7200 STAT 610 LINB29 DSM-5 COMP3161 EEEN40010 MATH 4431 K353 STA 3386 IERG4300 COMS W4167 ENG5298 AMME 2302 CS3910 COMPSCI 320 STATS 369 GR5242 COSC 328 CSCI435 MGTS1301 INFS2200 COMP3900 CIS 375 Module AE03 COMP3121 CS260 HAM503 MGMT5050 INT3075 COSC 285 GEOL0029 GEGE2X01 STAT1201 MATH1061 MMF1941H STAT 5060 CS 520 COMP 4320 MSIN0104 000T FINS3648 ECMT2160 ECON4003 Phys 129L CSE 142 CS 3130 MGEB01 EECS 340 Finance (20443/20444) ECMM149 COMP5310 EEEN60180 CSC 111 AT2 CSCI 4430 STAB57 MA/CSC 427 MATH322 D100 CSCI544 CITS3004 CI6227 CSE 565 APCO 1P01 852L1 ELEC S411F COMP3207 STATS330 ECON7530 FIT5149 CSI4104 CMPT 371 COMP201 SEHS4696 FI4003 MATH6182 CG1 WS MATH401 MGT 205 QTM 110 COMP 0137 MACE12201 FIT5210 ECE 544 BISM7206 HUDM 6055 ECON3203 STATS 210 MSCI 570 MATH6173 COMPSCI4039 Accounting COM3503 AOE2024 ECON213 PSYC10004 Control Data 100/200A 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