MODULE 4: INFERENTIAL STATISTICS AND HYPOTHESIS TESTING

Module 4: Inferential Statistics and Hypothesis Testing

By:Engr. Franz Johann B. De Vera, EngrD

• Explain inferential statistics and its importance

• Identify various sampling techniques and determine appropriate sample sizes

• Construct and interpret confidence intervals

• Perform hypothesis testing using t-tests, chi-square tests, and ANOVA

• Apply inferential statistics to engineering case studies

LEARNING OUTCOMES

WHAT IS INFERENTIAL STATISTICS?

• Uses sample data to make inferences about a population

• Difference between Descriptive vs. Inferential Statistics

• Example: Predicting election results based on exit polls

TYPES OF SAMPLING TECHNIQUES

EVERY INDIVIDUAL HAS A EQUAL CHANCE

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RANDOM SAMPLING

POPULATION DIVIDED INTO SUBGROUPS

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STRATIFIED SAMPLING

GROUPS SELECTED RANDOMLY

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CLUSTER SAMPLING

EVERY NTH ELEMENT SELECTED

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SYSTEMATIC SAMPLING

CHOOSE AVAILABLE SUBJECTS.

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CONVENIENCE SAMPLING

SAMPLE SIZE DETERMINATION

SAMPLE SIZE

Confidence Intervals and Estimation

STEPS IN HYPOTHESIS TESTING

4. COMPARE WITH CRITICAL VALUE OR P-VALUE
   

5. DRAW CONCLUSIONS

3. SELECT THE TEST AND COMPUTE THE TEST STATISTICS

STEPS IN HYPOTHESIS TESTING

T- TEST

COMPARES MEANS BETWEEN GROUPS

COMPARE ONE SAMPLE MEAN TO KNOWN POPULAR MEANN

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ONE SAMPLE T-TEST

COMPARE TWO INDEPENDENT GROUPS

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INDEPENDENT T-TEST

COMPARE MEANS WITHIN THE SAME GROUP

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PAIRED T-TEST

CHI-SQUARE TEST

TEST RELATIONSHIP BETWEEN CATEGORICAL VARIABLES

FORMULA:

ANOVA
( ANALYSIS OF VARIANCE)

COMPARES MEANS ACROSS THREE OR MORE GROUPS

ONE INDEPENDENT VARIABLE

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ONE WAY ANOVA

TWO INDEPENDENT VARIABLE

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TWO WAY ANOVA

ENGINEERING CASE STUDIES

USING HYPOTHESIS TESTING TO IDENTIFY DEFECTIVE PARTS

QUALITY CONTROL IN MANUFACTURING

CONFIDENCE INTERVALS TO ESTIMATE BEAM STRENGTH

​STRUCTURAL ENGINEER

ANOVA TO COMPARE CIRCUIT PERFORMANCE UNDER DIFFERENT CONDITIONS

​​ELECTRICAL ENGINEER

SUMMARY

4. HYPOTHESIS TESTING VALIDATES STATISTIC CLAIMS

5. STATISTICAL INFERENCE IS WIDELY USED IN ENGINEERING APPLICATIONS

1. INFERENTIAL STATISTICS HELPS IN DECISION MAKING

2. SAMPLING TECHNIQUE ENSURE DATA REPRESENTATIVE.

3. CONFIDENCE INTERVALS PROVIDES ESTIMATION RANGE