BSTAT Final

Nominal level of measurement

Represented by labels or names, they have nor order, and they can only be classified or counted.

Nominal

colors, gender, blood type, nationality, etc.

Ordinal level of measurement

Based on relative ranking or rating of items based on a defined attribute or qualitative variable. Variables based on this level of measurement are only ranked or counted.

What is the lowest level of measurement?

nominal

NOIR - nominal, ordinal, interval, ratio

Levels of measurement from lowest to highest

Ordinal

customer satisfaction ratings (very dissatisfied, dissatisfied, neutral, satisfied, very satisfied), educational levels (high school, bachelor's degree, master's degree), or pain levels (no pain, mild pain, moderate pain, severe pain)

Interval level of measurement

The distance between values is meaningful. Based on a scale with a known unit of measure. No absolute zero exists.

Interval

temperature, dress size, credit score, etc.

Ratio level of measurement

Based on a scale with a known unit of measurement and meaningful interpretation of zero on the scale.

Ratio

wages, units of production, weight, changes in stock prices, distance to class, etc.

Descriptive statistics

methods of organizing, summarizing, and presenting data in an informative way, mean, median, mode, etc.

Mean, median, & mode

measures of central tendency

Range, standard deviation, & variance

measures of dispersion

Inferential statistics

methods used to estimate a property of a population on the basis of a sample

Mode

Which measure of central tendency can be used for all levels of measurement?

Parameter

A characteristic of a population

Statistic

A characteristic of a sample

To compute mean, data must be measure at which level?

Interval or ratio

Discrete random variable

A random variable that can assume only certain clearly separated values.

Continuous random variable

A random variable that may assume an infinite number of values within a given range.

Standard normal probability distribution

mean equal to 0 and variance equal to 1

Simple random sample

A sample selected so that each item or person in the population has the same probability or chance of being included.

Systematic random sampling

A random starting point is selected, and then every kth member of the population is selected.

Stratified random sampling

A random starting point is selected, and then every kth member of the population is selected.

Cluster sampling

A population is divided into clusters using naturally occurring geographic or other boundaries. Then, clusters are randomly selected and a sample is collected by randomly selecting from each cluster.

Sampling error

The difference between the sample estimate and the actual population parameter, which may occur due to chance.

Central limit theorem

If all samples of a particular size are selected from any population, the sampling distribution of the sample mean is approximately a normal distribution. This approximation improves with larger samples.

Hypothesis testing

A procedure based on sample evidence and probability theory to determine whether the hypothesis is a reasonable statement.

Null hypothesis

A statement about the value of a population parameter developed for the purpose of testing with sample data that typically asserts no effect or no difference.

Level of significance

The probability of rejecting the null hypothesis when it is true.

Test statistic

A value, computed from sample information, used to determine whether to reject the null hypothesis.

Critical value

The dividing point between the region where the null hypothesis is rejected and the region where it is not rejected.

Type 1 error

Rejecting the null hypothesis, H0, when it is true.This type of error indicates a false positive result, where we conclude there is an effect or difference when, in fact, none exists.

alpha

The probability of making a Type I error, represented by the Greek letter

beta

The probability of making a Type II error, represented by the Greek letter

Type II error

Not rejecting the null hypothesis when it is false.

P-value

The probability of observing a sample value as extreme as, or more extreme than, the value observed, given that the null hypothesis is true.

Blocking variable

A second treatment variable that when included in the ANOVA analysis will have the effect of reducing the SSE term.

Correlation coefficient

A measure of the strength of the linear relationship between two variables.

characteristics of correlation coefficient

identified by the lowercase letter r, It ranges from −1 up to and including +1, A value near 0 indicates there is little linear relationship between the variables, A value near 1 indicates a direct or positive linear relationship between the variables, A value near −1 indicates an inverse or negative linear relationship between the variables.

coefficient of determination

The proportion of the total variation in the dependent variable Y that is explained, or accounted for, by the variation in the independent variable X.

Multicollinearity

exists when independent variables are correlated