Statistics Flashcards
Population mean (Formula)
Population variance (Formula)
Sample mean (Formula)
The sample mean estimator is unbiased
Sample variance - unbiased (Formula)
Generalisability (Def)
Results from statistical inference are generalisable when estimates obtained from a sample are reflective of the target population’s parameter
Sampling distribution (Def)
If we take several samples from a population, the sample estimates will differ due to sampling variation. The sampling distribution is the distribution of the sampling estimates
Standard error (Def)
The standard dev of the sampling distribution is a measure of the sampling variation and it’s called Standard error
Sampling methods - non-probability (Types)
- Convenience
- Systematic
- Purposive
- Quota
Sampling methods - probability (Types)
- Random
- Cluster
- Stratified
Convenience sampling
A type of non-probability sampling.
Sampling based on how convenient the subjects are to find.
Pro:
- Affordable, easy and quick
- Works ok if the population is homogeneous
Con:
- Not representative if the population is heterogeneous
Purposive sampling
A type of non-probability sampling.
The researcher relies on their own knowledge when choosing members of the population.
Pro:
- Beneficial when we want to access a subset of the population
Con:
- Requires domain knowledge
- Might not be representative
Quota sampling
A type of non-probability sampling.
Tailors the sample to be in proportion to some known characteristic of the population.
Pro:
- Affordable, easy and quick
- Accounts for differences in groups (strata)
Con:
- Selection bias if convenience sampling
- Needs prior knowledge to know the strata
Systematic sampling
A type of non-probability sampling.
Sampling at regular intervals, one every k=n/N
Pro:
- Can extend the sampling procedure to whole population (i.e. more representative)
Con:
- Needs knowledge of the whole population
- The order of the units can cause systematic bias
Bias of an estimator (Formula)
Precision of an estimator (Formula)
Mean Squared Error (Formula)
Population total (Formula)
Variance of the sample mean, for finite populations (Formula)
Stratified sampling (Def)
If the population of interest is heterogeneous with respect to the characteristic (parameter) of interest, one sampling procedure that can increase PRECISION is Stratified sampling.
Def: Partitioning a population into non-overlapping groups and sampling within each group. Each group is called a STRATUM.
If the sampling is done randomly, it’s called Stratified random sampling
Stratified sampling (Principles)
(1) Strata should be non-overlapping
(2) Strata should form a partition of the total pop
(3) Units within a stratum should be more similar to each other than others w/ respect to the characteristic of interest
(4) We should aim for homogeneity within strata, relative to the pop
(5) Success depends on the choice of characteristic used to partition the pop
Sampling fraction of the stratum (Formula)
Proportionate stratification (Def)
Each strata is represented in the sample in proportion to (see pic)
W_i = N_i / N
is the proportion of the Pop. within stratum i
Strata estimator of the population mean (Formula)
The estimator is unbiased.
W_i = N_i / N