Descriptive and Inferential Statistics
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This document explains the two major areas of statistics: descriptive statistics, which focuses on summarizing and presenting data, and inferential statistics, which involves making predictions and inferences from data. It elaborates on common problems solved using both areas, examples of data presentation, measures of central tendency and variation, hypothesis testing, and the application of Slovin's formula for sample size calculation. The document serves as a primer on the fundamental concepts and techniques used in statistical analysis.
Descriptive and Inferential Statistics
- 1. DESCRIPTIVE STATISTICS AND INFERENTIAL STATISTICS Prepared by: Danica A. Antiquina
- 2. “statistics is a branch of applied mathematics That deals with the collection, organization, presentation, analysis, and interpretation of data.” 2
- 3. Two major areas of statistics ✘ Descriptive Statistics It deals with the collection and presentation of data and summarizing values that describe the group’s characteristics. ✘ Inferential Statistics It deals with predictions and inferences based on the analysis and interpretation of the results of the information gathered by the statistician. 3
- 4. Common Problems ✘ Descriptive Statistics What is the percentage of X, Y, and Z participants? What is the average monthly salary of the employees in Company A? How much students in SRCB are satisfied about the quality education it provides? ✘ Inferential Statistics Is the claim true that the mean lifespan of the batter-operated toy cars is 5 years? Is the claim true that the student’s performance in Biology did not improve? Is there a significant difference in the mean sales of the three candidates for promotion? 4
- 5. ✘ Descriptive Statistics You could make a bar chart of yes or no answers. ✘ Inferential Statistics You could use your research to reason that around 75-80% of the population (all shoppers in all malls) like shopping at Prince Hypermart. 5 Example: You might stand in a mall and ask a sample of 100 people if they like shopping at Prince Hypermart.
- 6. DESCRIPTIVE STATISTICS It organize, analyze, and present data in a meaningful way. Differences Based on WHAT IT DOES? INFERENTIAL STATISTICS Compares, test and predicts data. 6
- 7. DESCRIPTIVE STATISTICS ✘ Measures of Central Tendency ✘ Measures of Variation Differences Based on tools INFERENTIAL STATISTICS ✘ Hypothesis Testing ✘ Analysis of Variance 7
- 8. Measures of Central Tendency: Mean, median, mode
- 9. FORMULAS: 𝝁 = 𝒙 𝑵 𝒙 = 𝒙 𝒏 9 𝑴𝒅 = 𝒎𝒆𝒅𝒊𝒂𝒏
- 10. Measures of Variations: range, variance, standard deviation
- 11. FORMULAS: 𝑹 = 𝑯𝒊𝒈𝒉𝒆𝒔𝒕 𝒔𝒄𝒐𝒓𝒆 − 𝑳𝒐𝒘𝒆𝒔𝒕 𝒔𝒄𝒐𝒓𝒆 11 𝝈 = 𝜎𝑁 2 𝒔 = 𝑠𝑁−1 2
- 13. 6 Steps in Hypothesis Testing 13 ✘ Identify the Problem ✘ Formulate Null and Alternative Hypothesis ✘ Level of Significance ✘ Statistics ✘ Decision Rule ✘ Conclusion
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- 16. DESCRIPTIVE STATISTICS Uses charts, graphs, and table. Differences Based on form of final result INFERENTIAL STATISTICS Uses probability. 16
- 18. SLOVIN’S FORMULA 18 ✘ If the population is very large, this formula will be used: 𝒏 = 𝑵 𝟏 + 𝑵𝒆𝟐 Where 𝑛 = sample size 𝑁 = number os cases 𝑒 = margin of error
- 19. Example: Using SLOVIN’S FORMULA 19 ✘ A researcher wants to know the average income of the families living in Barangay A which has 2,500 residents. Calculate the sample size the researcher will need if a 5% margin of error is allowed. 𝒏 = 𝟐, 𝟓𝟎𝟎 𝟏 + 𝟐, 𝟓𝟎𝟎 𝟎. 𝟎𝟓 𝟐 = 𝟑𝟒𝟒. 𝟖 ≈ 𝟑𝟒𝟓 𝒇𝒂𝒎𝒊𝒍𝒊𝒆𝒔 Where 𝑛 = sample size 𝑁 = 2,500 𝑒 = 0.05
- 20. 20 THANKS!