CHAPTER 16 THE FURTHER DATA ANALYSIS
CHAPTER 16 THE FURTHER DATA ANALYSIS
16.1 Introduction Initial Data Analysis Further Data Analysis Yes Describe Relationship
16.1 Introduction
16.2 FURTHER DATA ANALYSIS: ( MEASURED V ATTRIBUTE) o FDa is procedure that enables a decision to be made, based on the sample evidence oo There is no relationship s There is a relationship o these statistical procedures are called hypothesis tests
16.2 FURTHER DATA ANALYSIS: (MEASURED V ATTRIBUTE) ❖ FDA is procedure that enables a decision to be made, based on the sample evidence: There is no relationship There is a relationship ❖ These statistical procedures are called hypothesis tests
冷 Hypothesis osA statement about a population developed for purpose of testing 冷 Hypothesis tests ooA Procedure based on sample evidence and probability theory to determine whether the hypothesis is a reasonable statement o Four stages of hypothesis tests ≈ s Stage1: Specifying the hypotheses ≈ s Stage2 Defining the test parameters and the decision rule s Stage 3 EXamining the sample evidence ≈ s Stage4 The conclusions
❖ Hypothesis A statement about a population developed for purpose of testing. ❖ Hypothesis tests A Procedure based on sample evidence and probability theory to determine whether the hypothesis is a reasonable statement. ❖ Four stages of hypothesis tests Stage 1: Specifying the hypotheses. Stage 2: Defining the test parameters and the decision rule. Stage 3: Examining the sample evidence. Stage 4: The conclusions
o FDA for Measured v attribute requires two different hypotheses tests Two levels of attribute explanatory variable os three or more levels of attribute explanatory varlable
❖ FDA for Measured v Attribute requires two different hypotheses tests Two levels of attribute explanatory variable three or more levels of attribute explanatory variable
16 3 HYPOTHESIS TEST 1 Measured Response v Attribute Explanatory Variable with exactly two levels ☆Ⅲ lustrative Example s Response Variable: AMOUnT Spent on clothes per month s Attribute Explanatory Variable GENDER (Male/Female oo If Males and Females have the same ' spending on clothes characteristics then the average amounts spent monthly by males and by Female should be the same oo If Male and Females have different spending on clothes characteristics then the average amount spent monthly by Males and Female would be different
16.3 HYPOTHESIS TEST 1 Measured Response v Attribute Explanatory Variable with exactly two levels ❖ Illustrative Example Response Variable: AMOUNT Spent on Clothes per month Attribute Explanatory Variable GENDER (Male/Female) If Males and Females have the same 'spending on clothes' characteristics then the average amounts spent monthly by Males and by Female should be the same. If Male and Females have different 'spending on clothes' characteristics then the average amount spent monthly by Males and Female would be different
o Total population can be split into two or more sub-populations according to the level of the attribute, a population of Males and a population of Females
❖ Total population can be split into two or more sub-populations according to the level of the attribute, a population of Males and a population of Females
POPULATION MEANS THE SAME AmALE MALE ↓ AMOUNT POPULATION MEANS DIFERENT MALE PEALE MOUNT
POPULATION MEANS THE SAME
o Stage 1: Specifying the hypotheses 06 NULL HYPOTHESIS: Hl0:;0= ALTERNATIVE HYPOTHESIS H1:1≠1
❖ Stage 1: Specifying the hypotheses. NULL HYPOTHESIS: ALTERNATIVE HYPOTHESIS 0 0 1 H : = 1 0 1 H :
Stage 2: The Decision Rule os Results of ida for Illustrative Example 6 Outcome 1 Male Mean=￡45( Stand dev=￡20 Female mean=￡55( Stand dev=￡20) noenough evidence to form a clear judgement ☆ FDA is required MALD WALE AMOUNT 25
❖ Stage 2: The Decision Rule Results of IDA for Illustrative Example Outcome 1 ❖Male Mean = £45 (Stand Dev = £20) ❖Female Mean = £55 (Stand Dev = £20) ❖Noenough evidence to form a clear judgement ❖FDA is required