HYPOTHESIS TESTING Null Hypothesis and Research Hypothesis ?
Hypothesis testing
-
Upload
shameer-p-hamsa -
Category
Education
-
view
2.814 -
download
1
description
Transcript of Hypothesis testing
dept
. of f
utur
es s
tudi
es 2
010-
'12
Hypothesis Testing-Chi-Square Test
SHAMEER P.H
dept
. of f
utur
es s
tudi
es 2
010-
'12
REWIND YOUR MIND
Hypothesis- mere assumption to be proved or
disproved normal question that intends to resolve tentative formulated for empirical testing tentative answer to research question point to start a research
dept
. of f
utur
es s
tudi
es 2
010-
'12
Research Questions and Hypotheses
• Research question:• Non-directional:
• No stated expectation about outcome• Example:
• Do men and women differ in terms of conversational memory?
• Hypothesis:• Statement of expected relationship
• Directionality of relationship• Example:
• Women will have greater conversational memory than men
dept
. of f
utur
es s
tudi
es 2
010-
'12
The Null Hypothesis
• Null Hypothesis - the absence of a relationship• E..g., There is no difference between men’s and women’s
with regards to conversational memories• Compare observed results to Null Hypothesis• How different are the results from the null hypothesis?
• We do not propose a null hypothesis as research hypothesis - need very large sample size / power• Used as point of contrast for testing
dept
. of f
utur
es s
tudi
es 2
010-
'12
Hypotheses testing• When we test observed results against null:• We can make two decisions:
• 1. Accept the null• No significant relationship• Observed results similar to the Null Hypothesis
• 2. Reject the null• Significant relationship• Observed results different from the Null Hypothesis
• Whichever decision, we risk making an error
dept
. of f
utur
es s
tudi
es 2
010-
'12
Type I and Type II Error• 1. Type I Error• Reality: No relationship• Decision: Reject the null
• Believe your research hypothesis have received support when in fact you should have disconfirmed it
• Analogy: Find an innocent man guilty of a crime• 2. Type II Error• Reality: Relationship• Decision: Accept the null
• Believe your research hypothesis has not received support when in fact you should have rejected the null.
• Analogy: Find a guilty man innocent of a crime
dept
. of f
utur
es s
tudi
es 2
010-
'12
Potential outcomes of testingDecision
Accept Null Reject Null
R No E RelationshipALITY Relationship
Type II Error Correctdecision
Type I Error Correctdecision
dept
. of f
utur
es s
tudi
es 2
010-
'12
Start by setting level of risk of making a Type I Error• How dangerous is it to make a Type I Error:• What risk is acceptable?:
• 5%? • 1%?• .1%?
• Smaller percentages are more conservative in guarding against a Type I Error
• Level of acceptable risk is called “Significance level” :• Usually the cutoff - <.05
dept
. of f
utur
es s
tudi
es 2
010-
'12
Steps in Hypothesis Testing1) State research hypothesis2) State null hypothesis3) Decide the appropriate test criterion( eg. t test, χ2 test, F test
etc.)4) Set significance level (e.g., .05 level)5) Observe results6) Statistics calculate probability of results if null hypothesis
were true7) If probability of observed results is less than significance
level, then reject the null
dept
. of f
utur
es s
tudi
es 2
010-
'12
Guarding against Errors
• Significance level regulates Type I Error• Conservative standards reduce Type I Error:• .01 instead of .05, especially with large sample
• Reducing the probability of Type I Error:• Increases the probability of Type II Error
• Sample size regulates Type II Error• The larger the sample, the lower the probability of Type II Error
occurring in conservative testing
dept
. of f
utur
es s
tudi
es 2
010-
'12
Methods used to test hypothesis
T testZ testF testχ2 test……..
dept
. of f
utur
es s
tudi
es 2
010-
'12
Testing hypothesis for two nominal variablesVariables Null hypothesis ProcedureGender
Passing is not Chi-squarerelated to gender
Pass/Fail
dept
. of f
utur
es s
tudi
es 2
010-
'12
Testing hypothesis for one nominal and one ratio variableVariables Null hypothesis ProcedureGender
Score is not T-testrelated to gender
Test score
dept
. of f
utur
es s
tudi
es 2
010-
'12
Testing hypothesis for one nominal and one ratio variableVariable Null hypothesis ProcedureYear in school
Score is notrelated to year in ANOVAschool
Test score
• Can be used when nominal variable has more than two categories and can include more than one independent variable
dept
. of f
utur
es s
tudi
es 2
010-
'12
Testing hypothesis for two ratio variablesVariable Null hypothesis ProcedureHours spentstudying Score is not
related to hours Correlation
spent studyingTest score
dept
. of f
utur
es s
tudi
es 2
010-
'12
Testing hypothesis for more than two ratio variablesVariable Null hypothesis ProcedureHours spentstudying Score is positively
related to hoursClasses spent studying and Multiple missed negatively related regression
to classes missedTest score
dept
. of f
utur
es s
tudi
es 2
010-
'12
Chi square (χ2 ) test
dept
. of f
utur
es s
tudi
es 2
010-
'12
Used to:
• Test for goodness of fit• Test for independence of attributes• Testing homogeneity• Testing given population variance
dept
. of f
utur
es s
tudi
es 2
010-
'12
Chi-Square Test of Independence
dept
. of f
utur
es s
tudi
es 2
010-
'12
Introduction (1)
•We often have occasions to make comparisons between two characteristics of something to see if they are linked or related to each other.
• One way to do this is to work out what we would expect to find if there was no relationship between them (the usual null hypothesis) and what we actually observe.
dept
. of f
utur
es s
tudi
es 2
010-
'12
Introduction (2)
• The test we use to measure the differences between what is observed and what is expected according to an assumed hypothesis is called the chi-square test.
dept
. of f
utur
es s
tudi
es 2
010-
'12
For Example
• Some null hypotheses may be:
• ‘there is no relationship between the subject of first period and the number of students absent in our class’.
• ‘there is no relationship between the height of the land and the vegetation cover’.
• ‘there is no connection between the size of farm and the type of farm’
dept
. of f
utur
es s
tudi
es 2
010-
'12
Important• The chi square test can only be used on data that has the following
characteristics:
The data must be in the form of frequencies
The frequency data must have a precise numerical value and must
be organised into categories or groups.
The total number of observations must be greater than 20.
The expected frequency in any one cell of the table must be greater than
5.
dept
. of f
utur
es s
tudi
es 2
010-
'12
Contingency table
• Frequency table in which a sample from a population is classified according to two attributes, which are divided in to two or more classes
DRUNKARDS NON DRUNKARDSGENDER
MALES675 987
FEMALES540 997
dept
. of f
utur
es s
tudi
es 2
010-
'12
Degrees of Freedom
no of independent observations Number of cells – no. of constraints
dept
. of f
utur
es s
tudi
es 2
010-
'12
Formula
χ 2 = ∑ (O – E)2
E
χ2 = The value of chi squareO = The observed valueE = The expected value∑ (O – E)2 = all the values of (O – E) squared then added together
dept
. of f
utur
es s
tudi
es 2
010-
'12
Critical region:
dept
. of f
utur
es s
tudi
es 2
010-
'12
dept
. of f
utur
es s
tudi
es 2
010-
'12
Construct a table with the information you have observed or obtained.
Observed Frequencies (O)
Money
Health Love Row Total
men 82 446 355 883
women 46 574 273 893
Column total
128 1020 628 1776
dept
. of f
utur
es s
tudi
es 2
010-
'12
• Work out the expected frequency.
Expected frequency = row total x column total
Grand total
money health love Row Total
men 63.63 507.128 312.23 883
women 64.36 512.87 315.76 893
Column Total
128 1020 628 1776
dept
. of f
utur
es s
tudi
es 2
010-
'12
• For each of the cells calculate.
money
health love Row Total
Men 5.30 7.37 5.85
women 5023 7.29 5.8
Column Total
χ2Calc. =
36.873
(O – E)2
E
dept
. of f
utur
es s
tudi
es 2
010-
'12
• χ2Calc. = sum of all ( O-E)2/ E values in the
cells. • Here χ 2
Calc. =36.873
Find χ 2critical From the table with degree of
freedom 2 and level of significance 0.05χ 2
Critical =5.99
dept
. of f
utur
es s
tudi
es 2
010-
'12
Χ2 table
dept
. of f
utur
es s
tudi
es 2
010-
'12
Conclusion
• Compare χ2Calc. and Χ2
critical obtained from the table
• If χ2Calc. Is larger than χ2
Critical. then reject null hypothesis and accept the alternative• Here since χ 2
Calc. is much greater than χ 2Critical, we can
easily reject null hypothesisthat is ; there lies a relation between the gender and choice of selection.
dept
. of f
utur
es s
tudi
es 2
010-
'12
Reference
• RESEARCH METHODOLGIES - L R Potti