Study for Statistics Test Level 2 (9)
previous page↓
Today's study is on "Inferential Statistics".
Population and Sample
A population refers to the entire set under analysis.
A sample is a subset taken from the population.
A sample survey aims to infer population characteristics from the sample.
Design of Study
Experimental Study
An experimental study allows researchers to determine the conditions.
Three principles, often attributed to Fisher, are crucial in experimental studies:
Fisher's Three Principles:
- Randomization
- Replication
- Local control
Observational Study
An observational study is one where researchers cannot set the conditions.
In observational studies, randomization is excluded from the three principles, leading to potential selection bias.
Methods of Sampling
Simple Random Sampling
Every individual has an equal probability of being selected, and every combination is equally likely.
Systematic Sampling
In systematic sampling, individuals in the population are numbered, and selections are made at regular intervals.
Stratified Random Sampling
Stratified random sampling involves selecting samples from specific subgroups, such as gender, age, or occupation. The goal is to increase accuracy by reducing variability.
Multistage Sampling
Multistage sampling involves selecting samples at various stages based on different criteria. While this method simplifies the sampling process, it may compromise accuracy.
Point Estimation and Interval Estimation
Point Estimation
Point estimation refers to using a single value from the sample as an estimate.
Order Statistic
When samples are arranged in order, it's termed "order statistic."
If the distribution is symmetrical, the median equals the mean.
Trimmed Mean
A trimmed mean is calculated by excluding an equal number of the highest and lowest values from the sample.
Consistency and Unbiasedness
An estimator should be consistent and unbiased.
Consistency means that as the sample size grows, the estimator approaches the parameter value.
Unbiasedness implies that the expected value of the estimator matches the parameter, regardless of sample size.
For instance, sample means or unbiased variances are unbiased estimators.
Standard Error
When comparing estimators, the one with less variability is superior.
This variability is termed "standard error," which uses the variance of the sample.
Interval Estimation
Interval estimation provides a range within which the estimator lies, based on two values from the sample.
For a normal distribution, the following formula indicates that the population mean lies within this range with 95% probability:
Today's study has concluded.
