Simple Random Sampling and Sampling Distribution
Simple Random Sampling Simple random sampling, also called chance selection, refers to a method of sample collection in which each element in the population is given an equal chance of being included in the sample. In other words, all the…
Sampling Error
Sampling error is the statistical error that occurs when an analyst selects a sample that is not representative of the population as a whole. In other words, it is the difference between the observed value of a sample statistic (mean,…
Simple Random vs. Stratified Random Sampling
Simple random and stratified random sampling are both sampling techniques used by analysts during statistical analyses. Simple Random Sampling Simple random sampling involves the selection of a sample from an entire population such that each member or element of the…
Time-series Data vs. Cross-sectional Data
Time-series Data Time-series data refers to a set of observations made over a given period of time at specific and equally-spaced time intervals. That the observations are made at specific points in time means time intervals are discrete.
The Central Limit Theorem
The central limit theorem asserts that when we have simple random samples each of size n from a population with a mean μ and variance σ2, the sample mean X approximately has a normal distribution with mean μ and variance…
Calculation and Interpretation of the Standard Error of the Sample Mean
The standard error (SE) of the sample mean refers to the standard deviation of the distribution of the sample means. It gives analysts an estimate of the variability they would expect if they were to draw multiple samples from the…
Desirable Properties of an Estimator
A point estimator (PE) is a sample statistic used to estimate an unknown population parameter. It is a random variable and therefore varies from sample to sample. A good example of an estimator is the sample mean x, which helps…
Point Estimate vs. Confidence Interval Estimate
Point Estimate A point estimate gives statisticians a single value as the estimate of a given population parameter. For example, the sample mean X̄ is the point estimate of the population mean μ. Similarly, the sample proportion p is a…
T-distribution
The student’s T-distribution is a bell-shaped probability distribution symmetrical about its mean. It is considered the best distribution to use for the construction of confidence intervals when:
Calculation and Interpretation of Confidence Intervals
Confidence interval (CI) refers to a range of values within which statisticians believe the actual value of a certain population parameter lies. It differs from a point estimate which is a single, specific numerical value.
