6 inferential statistics

Inferential statistics

is the process of generalizing or making conclusions about the target population based on results obtained from a sample. It is a branch of statistics that allows researchers to draw conclusions and make generalizations about a population based on data. It extends the analysis beyond the data at hand to support evidence-based decisions

Population

The entire group of individuals or observations under study.

Sample

A representative subset of the population used for statistical analysis.

Parameter

Numerical constant obtained by observing the total population. Parameters are usually unknown because the entire population is seldom studied.

Statistics

Numerical variable obtained by observing a random sample from the population.

Estimation

is the process by which a statistic computed for a random sample is used to approximate (estimate) the corresponding parameter.

Point Estimate

single numeric value used to approximate a population parameter.

Interval Estimate

a pair of numbers, a lower limit and an upper limit, which serve as the bounding values within which the parameter is expected to lie with a certain degree of confidence.

Unbiased

its expected value (mean) is equal to the parameter being estimated.

Precise

meaning it is repeatable because its standard error (standard deviation) is small.

Consistent

meaning its deviation from the parameter being estimated decreases as sample size increases.

Hypothesis

Defined simply as a statement about the population. It is usually concerned with the parameters of the population about which the statement is made.

Hypothesis Testing

A set of procedures that culminate in either the rejection or the non-rejection of the null hypothesis. The decision to reject or not reject the hypothesis is based on the probability of occurrence of the sample results if the null hypothesis were true.

Alternative Hypothesis (H₁)

The hypothesis proposed by the researcher; represents what the researcher aims to support.

what the investigator believes (hence, the research hypothesis).

Null Hypothesis (H₀)

The negation of the alternative hypothesis; represents no effect or no difference.

should always be framed in hopes of being able to reject it so that H₁ could be accepted.

Hypothesis Testing Decision

If the probability of the sample result under the null hypothesis is low, reject H₀ in favor of H₁; if high, do not reject H₀.

testable

describes the requirement that the hypothesis allows for a statistical assessment of the data against it.

Two-tailed test

states that there is a difference between the two groups.

One-tailed test

specifies the direction of the difference.

α

level of significance

is the probability of occurrence that is considered too low to warrant support of the hypothesis being true.

Type I Error (α)

error of rejecting a true null hypothesis.

Type II Error (β)

error of not rejecting a false null hypothesis.

Critical region (region of rejection)

is the set of values of the test statistic that lead to the rejection of the null hypothesis.
These values have a probability of occurrence less than or equal to the level of significance, α.