SBP_RM_parent) block in the chain. Timestamp: It is a system that verifies the data into the block and assigns a time or date of creation for digital documents. The timestamp is a string COURSEWORK_31052025.pptx
- 1. Title of Seminar: Testing of Hypothesis Using Various Tests (ANOVA, Chi-Square, etc.) Presented by: Phalke Sagar Balkrishna Ph.D. Scholar Department of Technology Shivaji University, Kolhapur
- 2. Introduction to Hypothesis Testing •What is a hypothesis? •Null vs. alternative hypothesis •Type I & II errors •Confidence level & p-value •Relevance in Computer Engineering (e.g., software performance)
- 3. What is a Hypothesis? What is a Hypothesis? A hypothesis is an assumption or claim made about a population parameter (e.g., average response time of a server). • Example: "The average execution time of Algorithm A is less than Algorithm B." Hypothesis testing helps us decide whether to accept or reject such claims using sample data.
- 4. Null vs. Alternative Hypothesis Hypothesis Symbol Description Null Hypothesis H₀ Assumes no effect, no difference – the status quo. Alternative Hypothesis H or Ha ₁ Represents a new claim or effect to be tested. Example: •H : Execution times of Algorithm A and B are equal. ₀ •H : Execution times of Algorithm A and B are ₁ different.
- 5. Type I and Type II Errors Type Description Risk Type I Error Rejecting H when it is ₀ actually true False Positive Type II Error Failing to reject H when H is ₀ ₁ actually true False Negative •Example in Software Testing: • Type I: Believing a new compiler improves performance when it doesn’t. • Type II: Missing a real improvement in performance.
- 6. Confidence Level & p-value •Confidence Level: Probability that the test results are correct (usually 95% or 99%). •p-value: The probability of observing the sample result if H is true. ₀ •If p-value ≤ α (significance level, e.g., 0.05) Reject H₀ . ₀ •Smaller p-value means stronger evidence against H₀.
- 7. Relevance in Computer Engineering •Hypothesis testing is applied in: •Software Performance: Is new code faster than the old version? •Usability Studies: Does UI version A result in fewer errors than version B? •Network Efficiency: Is one protocol significantly more efficient than another? •Bug Prediction: Does code complexity correlate with defect frequency?
- 8. Statistical Tests Overview Parametric vs. Non-Parametric Tests Feature Parametric Tests Non-Parametric Tests Assumptions Require normal distribution No assumption of distribution Data Type Interval or ratio scale Ordinal or nominal scale Examples t-test, Z-test, ANOVA Chi-square, Mann-Whitney, Kruskal-Wallis
- 9. One-tailed vs. Two-tailed Tests Type Purpose Example One-tailed Tests for difference in one direction Is A greater than B? Two-tailed Tests for any difference (either way) Is A different from B (more or less)? Choosing the Right Test Situation Suggested Test Comparing 2 means (normal data) t-test Comparing >2 means ANOVA Proportions or large sample mean Z-test Relationship between categories Chi-square test Comparing medians (non-normal data) Mann-Whitney / Kruskal-Wallis
- 10. Overview of Key Tests • t-test: Compares means of two groups (e.g., speed of Algorithm A vs. B). • Z-test: Similar to t-test but used for large samples or known variance. • ANOVA: Compares means of more than two groups (e.g., comparing 3 sorting algorithms). • Chi-square Test: • Goodness-of-fit: Is the observed distribution as expected? • Independence: Is there a relationship between two categorical variables?
- 11. Data Collection & Sampling Techniques Types of Data Type Description Example (Computer Engineering) Nominal Categories without order OS type: Windows, Linux, Mac Ordinal Ordered categories Bug severity: Low, Medium, High Interval Numeric data without true zero CPU temperature in °C Ratio Numeric data with a true zero CPU usage (%), execution time (ms)
- 12. Data Preprocessing Steps to clean and prepare data: • Remove noise or incorrect entries • Handle missing values • Normalize/standardize values • Convert categorical data (e.g., OS type) to numerical codes for analysis Example: Collecting CPU Performance Data •Objective: Compare average CPU usage under different applications. •Steps: • Select a random sample of systems. • Collect data: CPU usage %, app name, duration. • Preprocess: Remove outliers, fill missing values. • Analyze using ANOVA or t-test.
- 13. What is a Z-Test? What is a Z-Test? A Z-test is used to test hypotheses about population means or proportions, especially when the sample size is large (n ≥ 30) and population variance is known. Z-Test for Means Used to compare a sample mean with a known population mean. Formula: Where: •xˉ: sample mean •μ: population mean •σ: population standard deviation •n: sample size
- 14. Z-Test for Proportions Z-Test for Proportions Used to compare sample proportion (pp) to a known population proportion (PP). Formula: When to Use Z-Test •Large sample size (n 30 ≥ ) •Population standard deviation is known •Data follows a normal distribution Computer Engineering Example Scenario: A lab wants to verify if its computers have a higher average CPU clock speed than the market average of 2.4 GHz. •H₀: Mean = 2.4 GHz •H₁: Mean > 2.4 GHz •Use Z-test for one-tailed hypothesis with large sample data
- 15. What is a T-Test? A t-test is used to compare means when the sample size is small (n < 30) and the population standard deviation is unknown. Types of T-Tests 1. One-Sample T-Test Compares the sample mean to a known or hypothesized population mean. Example: Check if the average RAM in a lab differs from the industry average (e.g., 8 GB). Two-Sample (Independent) T-Test Compares means from two independent groups. Example: Compare execution time of Algorithm A vs. Algorithm B on different systems. Paired T-Test Compares means from the same group before and after an event or treatment. Example: Test if a new compiler improves performance: •Measure execution time before and after update on the same set of programs.
- 16. When to Use Each Test Type When to Use One-Sample Comparing sample mean to known population mean Two-Sample Comparing means from two unrelated groups Paired T-Test Comparing before/after or matched-pair observations Computer Engineering Example Scenario: You upgrade a compiler and want to know if it improves execution speed. •Use a paired t-test •Measure execution time of programs before and after the upgrade •H : No difference in mean times ₀ •H : Mean time after upgrade is lower ₁
- 17. Parametric Tests – ANOVA (Analysis of Variance) – I What is One-Way ANOVA? One-Way ANOVA is used to compare the means of three or more independent groups to determine if at least one group mean is significantly different. Why Not Multiple t-Tests? Using multiple t-tests increases the risk of Type I error. ANOVA controls this risk by comparing all groups at once. Assumptions of One-Way ANOVA 1.Independence of observations 2.Normal distribution of data in each group 3.Equal variances (homogeneity of variance) How It Works – F-Statistic ANOVA breaks total variance into: •Between-group variance (difference between group means) •Within-group variance (variation within each group) F-statistic is calculated as: F=Variance Within Groups/Variance Between Groups A higher F value suggests more significant group differences.
- 18. Computer Engineering Example Computer Engineering Example Scenario: You want to compare RAM usage of three text editors: VS Code, Sublime, Notepad++. • Groups: 3 different software • Measure: RAM usage (in MB) while opening a large file • H : All software have ₀ equal average RAM usage • H : At least one software has ₁ different average RAM usage Apply one-way ANOVA to determine if the difference is statistically significant. Parametric Tests – ANOVA – II What is Two-Way ANOVA? Two-Way ANOVA is used to study the effect of two independent variables (factors) on one dependent variable, and whether there's any interaction between them. Why Use Two-Way ANOVA? It allows you to: •Test the individual effects of two factors •Check for interaction effects (i.e., combined influence of the two factors)
- 19. Key Concepts • Main Effect: Impact of each factor independently • Interaction Effect: Impact of both factors together, beyond individual effects Structure of Two-Way ANOVA Table Source Explanation Factor A Effect of first independent variable Factor B Effect of second independent variable A × B Interaction Combined effect of A and B Error Random variation Total Total variation
- 20. Computer Engineering Example Scenario: You want to test how operating system (Windows, Linux) and application (Chrome, Firefox) affect CPU usage. • Factor A: Operating System (2 levels: Windows, Linux) • Factor B: Application (2 levels: Chrome, Firefox) • Dependent Variable: Average CPU usage (%)
- 21. Thanks to all