Analysis, Normal distribution, and statistical inference

Standard deviation

measures the spread of individual data points around the mean

Standard error

measures the spread of sample means, not individual data points

Normal distribution

• Bell-shaped Curve

• Symmetric Distribution

• Total area equals 100%

Confidence intervals

provides a range of plausible values for an unknown population parameter

Probability

Is a value between 0 and 1 that quantifies the likelihood of an event

Null hypothesis

no significant difference or relationship

Alternative hypothesis

there is a significant difference or relationship

Hypothesis testing

a formal procedure to make decisions about populations based on sample data

Continuous random variable

has an infinite number of possible values that can be represented by an interval on the number line

Continuous probability distribution

the probability distribution of a continuous random variable

Normal distribution

continuous probability distribution for a random variable, x

Normal curve

graph of a normal distribution

Inflection points

The points at which the curve changes from curving upward to curving downward are called the inflection points

Standard normal distribution

a normal distribution with a mean of 0 and a standard deviation of 1

Inferential statistics

using information obtained from a sample to make predictions and draw conclusions about a larger population

Estimation

calculating the value of a parameter of a population from observations of a sample drawn from the population

Point estimate

single value estimate

Interval estimate

range of values which are likely to include the population parameter

Hypothesis testing

the process by which we use samples to draw conclusions about the populations from which they are taken

Null hypothesis

the hypothesis of no difference or no effect

Alternative hypothesis

the research hypothesis

Level of significance

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

Test statistic

assesses how consistent the sample data are with the null hypothesis in a hypothesis test

Critical region

set of values of the test statistic which lead to the rejection of the null hypothesis

Statistical decision

deciding whether to reject or accept the null hypothesis based on the calculated test statistic

Degrees of freedom

the number of independent values that a statistical analysis can estimate

Confidence level

probability that a sample is true for the entire population from which it was sampled

Analysis of variance

performed by comparing two types of variation to test the hypothesis concerning the means

Oneway ANOVA

compares the means of three or more independent groups to determine if there is a statistically significant difference between the correspoinding population means

Two-way ANOVA

used to determine whether or not there is a statistically significant difference between the means of three or more independent groups that have been split on two variables