STEPS IN HYPOTHESIS TESTING

 

1.    Set up two opposing hypotheses

 

        a. Null Hypothesis                      H₀

 

 

·     Researcher’s interest in verifying H₀.

·     H₀ is either rejected or accepted.

·     H₀ contains an equality.

 

 

b. Alternative Hypothesis           H₁

 

·     Specifies the situation if H₀ is rejected

·     H₁ contains a inequality that is mutually exclusive of H₀

 

2.    Define a test statistic and its distribution under the null hypothesis.

 

TEST STATISTIC - formula telling us how to confront the null hypothesis with the evidence.

Examples of Test Statistics:

 

a.     Z:population is normally distributed.

b.     t: population is normally distributed, but unknown variance.

c.     X² (Chi²): sum of squares of independent standard normal random variables.

d.     P Value:  population is normally distributed.

 

3.    Define a boundary for dividing the TEST STATISTIC RESULT space into a region of rejection and a region of acceptance by determining the level of significance.

 

Also called Decision Rule used to accept or reject the Null Hypothesis.

 

Level of Significance (a) - Probability of a Type I error.

 

Type I Error - Rejecting the Null Hypothesis when it is true.

 

Decision Rule for P value:

If P < a reject null

        If P > a do not reject null

 

4.    Collect data and compute the sample value of the test statistic.

 

5.    Determine whether the test statistic has fallen into the rejection or acceptance region.

 

6.    State and interpret results.

 

 

 

P value is a new approach to hypothesis testing.

 

It is the observed/actual level of significance.

 

Actual probability of rejecting when it should be accepted.

 

If P < a reject

If P > a do not reject

 

STATISTICAL TESTS

 

1.     One sample t-test - test whether the mean of a single variable differences from a specified constant.

       

Examples:

Whether the average IQ score for children born prematurely have an average IQ of 100.

 

Or Income in US = $25000

 

Test Statistic = t-test

 

H₀ : M_x = X                   X = constant

 

H_A : M_x ¹ X

 

2.     Independent samples t-test - Compares means for 2 groups of cases.

 

Test Statistic = t-test

 

H₀ : M_x = M_y

 

H_A : M_x ¹ M_y

 

Regression Analysis

Test of relationship

Test of independence

 

Estimates the equation that gives the best linear relationship between 1 dependent variable and 1 or more independent variables.

 

Simple Regression (bivariate) - 1 dependent and 1 independent variable

 

Multiple Regression (multivariate) - 1 dependent and > 1 independent variables

 

Dependent Variable - variable you are interested in

explaining

 

                              - left hand side variable

-       Y variable

-  example – Earnings

 

Independent Variables - variables that have a possible effect on dependent variable

                             

- right hand side variables

-       X variables

-       Examples – Education

Age

Sex

 

II. Model

 

Y = B₀ + B₁X₁ + B₂X₂ + ... + E

 

Y = dependent variable

 

X₁, X₂, X₃,... = independent variables

 

B₀ = constant   (Y when X_i=0)

 

B₁, B₂, B₃,...= coefficients on X₁, X₂, X₃,...

 

B₁:  tells you the relationship between X₁ and Y.

relates how much Y varies as X1 varies by 1

unit.

E= error term

 

Example:

 

Price_House = B₀ + B₁ (SQFT) + B₂(Bedrooms) +

B₃(Baths) + E

 

Price_House = $129,062 + $154(SQFT)

- 21,588(Bedrooms)

- $12,193(Baths)

 

1 additional SQFT increases the price of a house, on average by $154, holding all other factors constant.

 

1 additional bedroom decreases the Price of a house by $21,588, on average holding all the factors constant.

 

Hypothesis Testing:

 

X₁ : H_o : B₁ = 0

               H_A : B₁ ¹  0

 

X₂ :         H₀ : B₂ = 0   

H_A : B₂ ¹  0