GEA1000 FINAL Cheat Sheet (DRAFT) by ethanbaka

- Sampling Process via a known randomised mechanism. The probab­ility of selection may not be the same throughout all units of the sampling frame. Element of chance in selection process eliminates biases associated with selection.

-Simple Random Sampling: A sample of size n is chosen from the sampling frame such that every unit has an equal chance to be selected, through RNG. Advantage: Good Repres­ent­ation, Disadv­antage: Non-re­sponse, time consuming, access­ibility of info

-Systematic Sampling:The xth unit is chosen from every n/k units •where x,k are chosen integers and n is the size of the sampling frame. k selection interval. Advantage: Simple Disadv­antage: Not good repres­ent­ation

-Stratified Random Sampling: The population is divided into groups (strata) and SRS is applied to each strata to form the sample. Ex: Sample count during GE. Advantage: Good repres­ent­ation Disadv­antage: Need info about sampling frame and strata.

-Cluster Sampling:The population is divided into similar clusters and a fixed number of clusters are chosen using SRS. Advantage: less tedious, time-c­ons­uming, costly. Disadv: High variab­ility if clusters are dissim­ilar, req larger sample size to achieve low margin of error.

- Conven­ience sampling: Subjects are chosen based on proximity and availa­bility (Mall surveys)
- Volunteer sampling: Subjects volunteer themselves into a sample (Online Polls)

0.Sampling frame ≥ population (Include people that used to be in popula­tion, duplicate, etc)
1.Prob­ability sampling method implem­ented (selection bias ↓)
2.Large sample size (varia­bility and random error ↓)
3.Minimise non-re­sponse

Catego­rical: Variables that take on mutually exclusive categories (eg colours of cars)
Numerical: Variables with numerical values where arithmetic can be performed meaningful (mass)

Ordinal: Catego­rical variables where there is some natural ordering (eg feeling on a scale of 1-5)
Nominal: Catego­rical variable where there is no intrinsic ordering (eg pet ownership in SG)
Discrete: Numerical variable with gaps in the set of possible numbers (eg no of members in fam, 3.75 doesnt exist)
Continuous: Numerical variable that can be all values in a given range Random: Numerical variable with probab­ilities assigned to each value (eg range of time from 0-5s, all possible values have meaningful intepr­eta­tion)

Experi­mental study: The indepe­ndent variable is intent­ionally manipu­lated to observe its effect on the dependent variable (change x to see change in y)
Observ­ational study: Indivi­duals are observed and variables are measured without any manipu­lation

Popula­tion: Entire group we wish to know something about
Sample: A proportion of the population selected in the study
Sampling frame: “Source Material” from which sample is drawn
Census: An attempt to reach out to the entire population of interest

rate(A | B) ≤ rate(A) ≤ rate(A | NB) or vice versa. This means: The closer rate(B) is to 100%, the closer rate(A) is to rate(A | B) If rate(B) = 50%, then rate(A) = 0.5[rate(A |B) + rate(A | NB)] If rate(A | B) = rate(A | NB), rate(A) = rate(A | B) = rate(A | NB)

Probab­ility in Indepe­ndent Event
For indepe­ndent events A and B: P(A) = P(A | B) P(A) × P(B) = P(A ∩ B)
Sensit­ivity and Specif­icity
Sensit­ivity = P(Test Positive | Individual is infected) Specif­icity = P(Test Negative | Individual is not infected)

Measure of the linear associ­ation between two variables
-1 ≤ r ≤ 1 •0 to ± 0.3 = weak, ± 0.3 to ± 0.7 = moderate, ± 0.7 to ± 1 = strong
Removing outliers can increase, decrease, or cause no change to r
r is not affected by interc­hanging the x and y variables r=Cov(­X,Y­)/S­Dx*SDy. Cov(X,­Y)=­Cov­(Y,X)
r is not affected by adding a number to all values of a variable. (eg y=2x, if +10 to allx,curve move right)
r is not affected by multip­lying a number to all values of a variable

An outlier is an observ­ation that falls well above or below the overall bulk of the data . A general rule is that outliers should not be removed unnece­ssarily x is an outlier if x > Q3 + 1.5·IQR or x < Q1 - 1.5·IQR.

Left skewed curve --> Peak on the right. Mean < Median < Mode

A third variable that is associated with both the indepe­ndent and dependent variables. When a confounder is present, segregate the data by the confou­nding variable. This method is called slicing

A phenomenon in which a trend appears in more than half of the groups of data but changes when the groups are combined

Rate(A | B) > rate(A | NB) ⟺ rate(B | A) > rate(B | NA)
Rate(A | B) < rate(A | NB) ⟺ rate(B | A) < rate(B | NA)
Rate(A | B) = rate(A | NB) ⟺ rate(B | A) = rate(B | NA)

Confidence interval is a range of values likely to contain a population parameter based on a certain degree of confidence We are 95% confident that the population parameter lies within the confidence interval Another interp­ret­ation is that 95% of the resear­chers who repeat the experiment will have intervals that contain the population parameter It is a common mistake to say that there is 95% chance that the population parameter lies within the confidence interv­alP­rop­erties of Confidence Intervals The larger the sample size, the smaller the random error and •narrower the confidence interval The higher the confidence level, the wider the confidence interval

pop'n mean = xbar +- t* x (s/root n)
pop'n propor­tion= p +- z x root(p(1-p)/n)

- The null hypothesis asserts the stand of no effect, meaning that the variances in the sample are not inherent in the population and occured by random chance when choosing sample
-The altern­ative hypothesis is what we wish to confirm and pit against the null hypothesis Through hypothesis testing, we wish to reject the null hypothesis in favour of the altern­ative hypothesis
-If p-value ≥ SL, do not reject null hypothesis

-Ecological Fallacy deduces the inferences on correl­ation about indivi­duals based on aggregated data (country with high average income, assumes indiv is wealthy)
-Atomistic Fallacy generalise the correl­ation based on indiv towards the aggregate level correl­ation
(eg one person with high education makes more money, means higher education in country will lead to higher national income)