Non-ProbabilitySampling
Population VS Sample
Experimental VS Observation
Properties of Experimental:
1.
Random Assignment (X Random Sampling)
Sorting of participants into Control and Treatment Group
randomly.*If the no. is large, the treatment and control
groups tends to be similar
1.
Binding
Subjects / Assessors don’t whether who are in the
treatment or control group
Placebo Effect
Placebo: Treatment with no active ingredients, and no
effect
Double Blinding
Both subjects and assessors are blinded
Eg. Target Population: Singaporeans residents
Sampling frame: Handphone users
Sampling frame > Target Population → Not all
Singapore No. holders are Singaporeans, or some
Singaporeans can own 2 phones.
Census VS Sample
Census: Whole Population
Sample: A Proportion of
population selected
Probability Sampling – probability of selection of
individuals within the sampling frame is known
and non-zero
Selection Bias
Non-response Bias
Researchers intentionally
pick a certain group
Sampling is skewed to a
certain group
Properties of Observation Experiment
1.
Random Sampling
2.
Presence of Control and treatment which are selfassigned
Let Spicy food be B and Female be A
Participants refused to
answer or response to the
survey
Rate (Female given that they like spicy food) = Rate (A|B)
=
𝑅𝑎𝑡𝑒 (𝐴∩𝐵)
𝑅𝑎𝑡𝑒 (𝐵)
Association:
It is between Rate (A|B) and Rate (A|NB)
Rate (A|B) + Rate (NA|B) = 1
Leading to:
Imperfect sampling
For positive association between A and B
Generalisation Criteria
Rate(A | B) > Rate (A | NB)
Rate(B | A) > Rate (B | NA)
Rate(NA | NB) > Rate (NA | B)
Rate(NB | NA) > Rate (NB | A)
1.
Good Sampling Frame
Sampling frame > population of interest
1.
Probability-based Sampling
2.
Large Sample Size
3.
Minimum Non-response
For negative association, the inequality sign is <
For no association between A and B:
Rate (A|B) = Rate (A|NB)
Sampling Plan
Simple
Random
Sample
Systematic
Sample
Advantages
Good representation of the
population
Disadvantages
Time-consuming;
accessibility of information
Simpler Selection as opposed
to Simple Random Sampling
Potentially
underrepresenting
the
population
Require Sampling frame
and
criteria
into
classification of population
into stratum
Require large sample size
in order to achieve low
margin of error
Stratified
Random
Sample
Good
representation
Sample by Stratum
of
Cluster
Random
Sample
Less time-consuming and less
costly
Symmetry Rules
Rate(A | B) < Rate (A | NB)
Rate(B | A) < Rate (B|NA)
Properties of Rate
Rate(A) = ?
Rate(A|B)
•
•
Rate(A|NB)
If Rate(A) = 50%, Rate (B) = 0.5 (Absolute no.- on
another line)
If Rate (A) > 50%, Rate (B) < 0.5
Simpson’s Paradox
Simpson’s Paradox is a phenomenon in which a trend appears in
more than half of the groups of data but disappears or reverses
when the groups are combined.
Confidence Interval
Correlation (r)
•
•
•
r is not affected by
Interchanging x and y
Adding/ subtracting a constant number to all values
Multiplying / Dividing positive no to all variable
A regression equation is for the average population, not
directed to a specific person.
∴ The regression equation cannot determine anything for
a person
Confounders
Therefore, the size of the stone is a confounders.
Co-founders must have association with the 2 variables
Presence of a Simpson’s Paradox → Confounder present
BUT
Having a confounder ≠ Have Simpson’s Paradox
Distribution Curve
Identifying Outlier
High outlier: > Q3 +1.5 x IQR
Low outlier: < Q3 -1.5 x IQR
How big numerical outliers affect mean, median and
standard deviation?
• Mean will increase greatly
• Median and IQR will remain approximately the same
• Standard deviation will decrease greatly (no matter
what type of outlier
If many samples are taken, 95% of the time, the sample
mean will fall within the population mean.
Variance
𝑠2 =
•
•
•
Spread Range
log 𝑒 𝑦 = 1.33
𝑦 = ⅇ0.33
Probability Rule
A and B are mutually exclusive = P(A∩B) / P(A and B) = 0
P(A∪B) / P(A or B) = P(A) + P(B)
A and B are independent: P(A∩B) = P(A) × P(B)
P(B | A) = P(B) P(A| B) = P(A)
𝑥,ҧ 𝜎 2
▪
Greater Variation → Fatter bell
shape
Greater number of participants
→ Narrower confidence interval
𝑥ҧ = mean
𝜎 = standard deviation
p-value < Value of significance → reject H0
The stronger the r value = the point are closer to the best fit line
𝑠
𝑅𝑖𝑠𝑒
m= 𝑠𝑦 𝑟
m= 𝑅𝑢𝑛
𝑥
x is used to predict y
2
𝑛−1
If the variance of x is zero, then xi = x for all i ranging
from 1 to n.
If all the values of x in the data set are multiplied by
2, then the variance is multiplied by 4.
Adding/ subtracting a constant to x will not change
variance
For “at least as extreme” questions,
1. Extreme value must include the sample value that is
stated In the question
2. Inequality follow the H1 definition
1.
2.
Properties of Mean, Median
Adding a constant (+/-) → change mean by that
constant value.
Multiply by constant → mean multiply by constant
Normal Distribution
▪
Regression
෌ 𝑥𝑖 − 𝑥ҧ
p-value = how likely is the data going to
occur under H0
1.
2.
Properties of Standard Deviation& IQR
Adding a constant (+/-) won’t change mean by
that constant value.
Multiply by constant (+/-) → mean multiply by
|constant|