Stats Exam 2

inferential statistics

A branch of statistics that allows researchers to make conclusions about a population based on a sample of data. It includes techniques such as hypothesis testing and confidence intervals.

measures of dispersion

statistical measures that describe the spread or variability of a dataset, including range, variance, and standard deviation.

boxplot

a graph that presents information about the central tendency and variation of a variable

Sample vs. population

Sample refers to a subset of individuals selected from a larger group (population), used to infer characteristics about the whole population.

statistic

a numerical value that summarizes or describes a characteristic of a sample, often used to estimate parameters of the population.

parameters

are mathematical characteristics of populations

EPSEM methods

(Equal Probability of Selection Method) are sampling techniques that ensure each member of the population has an equal chance of being selected in the sample.

sample

a subset of individuals or observations drawn from a larger population, used to estimate characteristics of the whole population.

cluster sample

a method of sampling by which geographical units are randomly selected and all cases within each selected unit are tested to represent a larger population

bias

an estimator is unbiased if the mean of its sampling distribution is equal to the population value of interest

Efficiency

the extent to which the sampling distribution is clustered around its mean

sample statistics that are unbiased and efficient

are preferred in statistical analysis because they provide accurate and reliable estimates of population parameters.

normal curve

properties, areas under the curve

Z- scores

are the scores that have been standardized to the theoretical normal curve it also represents how different a raw score is from the mean in standard deviation units

Sampling distribution

is the probability distribution of a statistic obtained through a large number of samples drawn from a specific population. It describes how the sample means vary from the population mean.

Central limit theorem

a theorem that specifies the mean, standard deviation, and shape of the sampling distribution, given that the sample is large

standard deviation of the sampling distribution (standard error of the mean)

it quantifies how much the sample mean is expected to vary from the true population

probability

is a measure of the likelihood that an event will occur

common confidence levels associated alphas

confidence levels are used to quantify the degree of certainty in an interval estimate ( 90%, 95%, 99%)

Estimation procedures

are statistical methods used to infer the characteristics of a population based on sample data, often involving point estimates and interval estimates.

interval estimates

a range of values within which the population parameter is likely to fall, with specific level of confidence

Point estimates

a single value used to approximate a population parameter

confidence intervals

an estimate of a population value in which a range of values is specified

Random sample

is a subset of individuals chosen from a larger population where each individual has an equal chance of being selected

Representative sample

is a subset of a population that accurately reflects the characteristics of the entire population

width of interval estimates

refers to the range of values within the confidence interval

interquartile range

is a measure of statistical dispersion and represents the range with which the middle 50% of the data values lie