STATISTICS REVIEWER

Hypothesis

In statistical reference, it is a statement or claim about characteristics of a population.

Hypothesis testing

A decision-making process for evaluating claims about a population parameter

Null hypothesis

Initial claim which the researcher tries to disprove, reject or nullify.

Alternative hypothesis

Contradicts the null hypothesis. Also known as research hypothesis.

Significance level

Probability of committing a Type I error, probability of rejecting the correct null hypothesis.

Confidence level

probability of not committing a Type II error

Type I error

True null hypothesis is incorrectly rejected, “false positive.”

Type II error

False null hypothesis is not rejected, “false negative.”

Test statistic

a rule, based on sample data, for deciding whether to reject null hypothesis

Z-test

Used for n>30 participants.

T-test

Used for n<30 participants.

Rejection region

Shaded area. When test statistic lies on rejection region, Ho will be rejected.

Critical Value

value that separates the non-rejection and rejection region. Also known as confidence coefficients.

Decision Rule

We reject the Ho if test statistic is > T tabular.

What formula is this?

Z-test formula

What formula is this?

T-test formula.

Population proportion

The number of members in the population with a particular attribute divided by the number of members in the population.

Two-tailed test

A test that uses keywords such as change, the same, different/difference.

One tailed test

A test that uses keywords such as increased, greater, larger, improved.

What formula is this?

Testing for single proportion.

Correlation Analysis

A statistical method used to determine whether a relationship between two variables exists. We can describe the realtionship between two variables.

Bivariate Data

Data that involve two variables; purpose of the analysis is to describe relationships. Two variables taken from sample or population.

What it’s important to know in correlation analysis?

1.) How strong the correlation is

2.) In which direction the correlation goes.

Positive correlation

exists when high values of one variable

correspond to high values in the

other variable or low values in

one variable correspond to low

values in the other variable.

Negative correlation

exists when high values in one

variable correspond to low values

in the other variable or low values

in one variable correspond to high

values in the other variable

Zero correlation

exists when high values in one variable

correspond to either high or low

values in the other variable.

Correlation Analysis Techniques

1.) Scatterplot Diagram

2.) Pearson Product-Moment Correlation Coefficient.

Scatterplot

shows how each point collected from a

set of bivariate data are scattered

on the Cartesian plane. It is a

graphical representation of the

relationship between two

variables.

Pearson R

It is the most commonly used

statistic to measure the degree of

relationship between two variables

Who developed the Pearson R

Karl Pearson.

Regression Analysis

When two variables are

significantly correlated, we can

predict the value of one

variable in terms of the other

variable. This process is called

regression analysis.

Testing the Significance of R

The computed correlation coefficient r should

be tested for significance.

❑If r is significant

then the relationship

between two variables exists in the actual

population.

❑If r is not significant

then the relationship is

due to chance alone, and it does not really

exist in the population.

What formula is this?

This is for testing the significance of R

What formula is this for? it also uses the formula for significance of r.

This is for regression analysis.

Y’= a+bX

Equation of regression line.