Different Statistical Tests overview
- One sample T-test
- Independent Samples T-test
- Paired sample T-test
Ans: Certainly! Below are five real-time examples for each of the three types of t-tests:
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Example: Exam Scores
- Scenario: You want to test whether the average score of a group of students in a class is significantly different from the expected mean score of 75.
- Hypothesis:
- Null Hypothesis (H0): The average score is 75.
- Alternative Hypothesis (H1): The average score is different from 75.
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Example: Customer Satisfaction
- Scenario: A company believes the average customer satisfaction rating is 8 on a scale of 1 to 10. You want to test if the average satisfaction is significantly different.
- Hypothesis:
- Null Hypothesis (H0): The average satisfaction is 8.
- Alternative Hypothesis (H1): The average satisfaction is different from 8.
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Example: Weight Loss Program
- Scenario: A weight loss program claims that participants will lose an average of 5 pounds after four weeks. You want to test if the program is effective.
- Hypothesis:
- Null Hypothesis (H0): The average weight loss is 5 pounds.
- Alternative Hypothesis (H1): The average weight loss is different from 5 pounds.
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Example: Delivery Time
- Scenario: A courier company states that the average delivery time is 48 hours. You want to test if the company is meeting this claim.
- Hypothesis:
- Null Hypothesis (H0): The average delivery time is 48 hours.
- Alternative Hypothesis (H1): The average delivery time is different from 48 hours.
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Example: Blood Pressure
- Scenario: A medical study claims that the average blood pressure of a population is 120 mmHg. You want to test if this claim holds true.
- Hypothesis:
- Null Hypothesis (H0): The average blood pressure is 120 mmHg.
- Alternative Hypothesis (H1): The average blood pressure is different from 120 mmHg.
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Example: Male vs. Female Salaries
- Scenario: You want to test if there is a significant difference in the average salaries of male and female employees in a company.
- Hypothesis:
- Null Hypothesis (H0): There is no difference in average salaries.
- Alternative Hypothesis (H1): There is a significant difference in average salaries.
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Example: Product A vs. Product B Sales
- Scenario: Two sales teams are selling different products. You want to test if there is a significant difference in the average sales between the two products.
- Hypothesis:
- Null Hypothesis (H0): There is no difference in average sales.
- Alternative Hypothesis (H1): There is a significant difference in average sales.
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Example: Test Scores of Students from Different Schools
- Scenario: You want to test if there is a significant difference in the average test scores of students from School A and School B.
- Hypothesis:
- Null Hypothesis (H0): There is no difference in average test scores.
- Alternative Hypothesis (H1): There is a significant difference in average test scores.
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Example: Effectiveness of Two Training Programs
- Scenario: Two training programs are implemented to improve employee productivity. You want to test if there is a significant difference in their effectiveness.
- Hypothesis:
- Null Hypothesis (H0): There is no difference in effectiveness.
- Alternative Hypothesis (H1): There is a significant difference in effectiveness.
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Example: Exam Performance of Students with and without Tutors
- Scenario: You want to test if there is a significant difference in the average exam scores between students who receive tutoring and those who do not.
- Hypothesis:
- Null Hypothesis (H0): There is no difference in average exam scores.
- Alternative Hypothesis (H1): There is a significant difference in average exam scores.
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Example: Before and After Weight Loss
- Scenario: You want to test if there is a significant difference in the weights of individuals before and after participating in a weight loss program.
- Hypothesis:
- Null Hypothesis (H0): There is no difference in weights before and after.
- Alternative Hypothesis (H1): There is a significant difference in weights before and after.
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Example: Blood Pressure Before and After Medication
- Scenario: Patients' blood pressure is measured before and after taking a new medication. You want to test if there is a significant change in blood pressure.
- Hypothesis:
- Null Hypothesis (H0): There is no difference in blood pressure before and after.
- Alternative Hypothesis (H1): There is a significant difference in blood pressure before and after.
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Example: Reaction Time Before and After Training
- Scenario: Participants undergo reaction time testing before and after a training program. You want to test if there is a significant improvement.
- Hypothesis:
- Null Hypothesis (H0): There is no difference in reaction time before and after.
- Alternative Hypothesis (H1): There is a significant difference in reaction time before and after.
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Example: Employee Productivity Before and After Software Upgrade
- Scenario: Productivity metrics are measured before and after upgrading office software. You want to test if there is a significant change in productivity.
- Hypothesis:
- Null Hypothesis (H0): There is no difference in productivity before and after.
- Alternative Hypothesis (H1): There is a significant difference in productivity before and after.
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Example: Pain Levels Before and After Treatment
- Scenario: Patients report pain levels before and after receiving a new treatment. You want to test if there is a significant reduction in pain.
- Hypothesis:
- Null Hypothesis (H0): There is no difference in pain levels before and after.
- Alternative Hypothesis (H1): There is a significant difference in pain levels before and after.
- One sample Z-test
- Two Samples Z-test
Ans: Certainly! Below are five real-time examples for each of the two types of Z-tests:
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Example: Average Height of a Population
- Scenario: You want to test if the average height of a population is significantly different from the national average height.
- Hypothesis:
- Null Hypothesis (H0): The average height is equal to the national average.
- Alternative Hypothesis (H1): The average height is different from the national average.
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Example: Average Call Duration
- Scenario: A call center claims that the average call duration is 5 minutes. You want to test if the average call duration is significantly different from this claim.
- Hypothesis:
- Null Hypothesis (H0): The average call duration is 5 minutes.
- Alternative Hypothesis (H1): The average call duration is different from 5 minutes.
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Example: Average Time to Complete a Task
- Scenario: An online platform claims that the average time to complete a specific task is 20 minutes. You want to test if users take significantly more or less time.
- Hypothesis:
- Null Hypothesis (H0): The average time is 20 minutes.
- Alternative Hypothesis (H1): The average time is different from 20 minutes.
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Example: Average Temperature
- Scenario: A meteorological department claims that the average temperature in a city is 25°C. You want to test if the actual average temperature is significantly different.
- Hypothesis:
- Null Hypothesis (H0): The average temperature is 25°C.
- Alternative Hypothesis (H1): The average temperature is different from 25°C.
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Example: Average Customer Satisfaction Score
- Scenario: A company claims that their average customer satisfaction score is 4.5 out of 5. You want to test if the average satisfaction is significantly different.
- Hypothesis:
- Null Hypothesis (H0): The average satisfaction score is 4.5.
- Alternative Hypothesis (H1): The average satisfaction score is different from 4.5.
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Example: Sales Performance of Two Products
- Scenario: You want to test if there is a significant difference in the average sales performance of Product A and Product B.
- Hypothesis:
- Null Hypothesis (H0): There is no difference in average sales performance.
- Alternative Hypothesis (H1): There is a significant difference in average sales performance.
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Example: Test Scores of Students from Two Schools
- Scenario: You want to test if there is a significant difference in the average test scores of students from School X and School Y.
- Hypothesis:
- Null Hypothesis (H0): There is no difference in average test scores.
- Alternative Hypothesis (H1): There is a significant difference in average test scores.
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Example: Employee Productivity Before and After Training (Two Groups)
- Scenario: Two groups of employees undergo different training programs, and you want to test if there is a significant difference in the improvement in productivity between the two groups.
- Hypothesis:
- Null Hypothesis (H0): There is no difference in improvement.
- Alternative Hypothesis (H1): There is a significant difference in improvement.
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Example: Average Monthly Spending of Two Customer Segments
- Scenario: You want to test if there is a significant difference in the average monthly spending of two customer segments (e.g., new customers vs. returning customers).
- Hypothesis:
- Null Hypothesis (H0): There is no difference in average monthly spending.
- Alternative Hypothesis (H1): There is a significant difference in average monthly spending.
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Example: Reaction Time of Two Groups under Different Conditions
- Scenario: You want to test if there is a significant difference in the reaction time of two groups of participants under different experimental conditions.
- Hypothesis:
- Null Hypothesis (H0): There is no difference in reaction time.
- Alternative Hypothesis (H1): There is a significant difference in reaction time.
Ans:Z-tests and t-tests are statistical methods used for hypothesis testing, specifically for comparing sample means. However, there are key differences between the two, and the choice between them depends on certain conditions related to the data.
- Z-Test: Requires knowledge of the population standard deviation.
- T-Test: Typically used when the population standard deviation is unknown and is estimated from the sample data.
- Z-Test: Ideally suited for large sample sizes (typically n > 30).
- T-Test: More robust for small sample sizes. It is commonly used when dealing with samples less than 30.
- Z-Test: Assumes a normal distribution of the data.
- T-Test: More robust and can be used even when the distribution of the data is not perfectly normal, especially with larger sample sizes.
- Z-Test: Typically used when the population parameters are known, or the sample size is large enough to assume normality.
- T-Test: Preferred when dealing with smaller sample sizes or when the population standard deviation is unknown.
- Z-Test: Often used for interval or ratio data.
- T-Test: Applicable to interval or ratio data and is commonly used when comparing means of two groups or assessing the significance of a single group mean.
- Z-Test: Does not involve degrees of freedom.
- T-Test: Involves degrees of freedom, which is a parameter that adjusts for the sample size in small samples.
- Z-Test: Uses the z-statistic, calculated as the difference between the sample mean and population mean divided by the standard error.
- T-Test: Uses the t-statistic, calculated similarly but with the sample standard deviation replacing the unknown population standard deviation.
- Z-Test: Used when comparing the average height of a sample to a known population average.
- T-Test: Used when comparing the average exam scores of two different groups of students.
- If the population standard deviation is known and the sample size is large, a Z-test is appropriate.
- If the population standard deviation is unknown or the sample size is small, a t-test is often more suitable.
In summary, the choice between a Z-test and a t-test depends on the characteristics of the data, such as the sample size and knowledge of the population standard deviation. Z-tests are appropriate for larger samples with known population standard deviations, while t-tests are more versatile and can handle smaller sample sizes and situations where the population standard deviation is unknown.
- Chi-square test for independence
- Chi-square goodness of fit test
Ans: The Chi-square test is a statistical test used to determine if there is a significant association between two categorical variables (Chi-square Test for Independence) or to assess how well the observed distribution of data fits an expected distribution (Chi-square Goodness of Fit Test). Here are five real-time examples for each:
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Example: Gender and Voting Preference
- Scenario: Investigating whether there is a significant association between gender (male or female) and voting preference (Candidate A, Candidate B, or Undecided) in an election.
- Hypothesis:
- Null Hypothesis (H0): Gender and voting preference are independent.
- Alternative Hypothesis (H1): There is a significant association between gender and voting preference.
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Example: Smoking Habits and Lung Cancer
- Scenario: Analyzing whether there is a significant association between smoking habits (smoker or non-smoker) and the incidence of lung cancer in a population.
- Hypothesis:
- Null Hypothesis (H0): Smoking habits and lung cancer incidence are independent.
- Alternative Hypothesis (H1): There is a significant association between smoking habits and lung cancer.
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Example: Educational Attainment and Job Satisfaction
- Scenario: Examining whether there is a significant association between educational attainment (high school, bachelor's, master's, Ph.D.) and job satisfaction level (low, medium, high) among employees.
- Hypothesis:
- Null Hypothesis (H0): Educational attainment and job satisfaction are independent.
- Alternative Hypothesis (H1): There is a significant association between educational attainment and job satisfaction.
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Example: Social Media Usage and Age Group
- Scenario: Investigating whether there is a significant association between social media usage frequency (low, medium, high) and age group (18-24, 25-34, 35-44, etc.).
- Hypothesis:
- Null Hypothesis (H0): Social media usage and age group are independent.
- Alternative Hypothesis (H1): There is a significant association between social media usage and age group.
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Example: Product Preference and Income Level
- Scenario: Analyzing whether there is a significant association between product preference (Product X, Product Y, or No Preference) and income level (low, medium, high) among consumers.
- Hypothesis:
- Null Hypothesis (H0): Product preference and income level are independent.
- Alternative Hypothesis (H1): There is a significant association between product preference and income level.
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Restaurant Menu Items:
- Scenario: A restaurant manager wants to ensure that the sales of different menu items align with the expected distribution. For instance, they expect 30% of sales from appetizers, 50% from main courses, and 20% from desserts.
- Data Collection: Record the actual sales percentages for each category over a specific period.
- Hypothesis: The observed distribution of sales across menu categories fits the expected distribution.
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Social Media Ad Campaigns:
- Scenario: A social media marketing team is running multiple ad campaigns targeting different demographics. They have an expected distribution of engagement rates across age groups.
- Data Collection: Collect the engagement rates from each age group for each ad campaign.
- Hypothesis: The observed distribution of engagement rates across age groups matches the expected distribution.
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Insurance Claims Types:
- Scenario: An insurance company expects a certain distribution of claims types, such as 40% for auto accidents, 30% for property damage, and 30% for health-related claims.
- Data Collection: Analyze a sample of recent insurance claims and categorize them into the expected types.
- Hypothesis: The observed distribution of claims types follows the expected distribution.
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Online Shopping Cart Abandonment Reasons:
- Scenario: An e-commerce site anticipates that 25% of cart abandonments are due to high shipping costs, 40% due to complicated checkout processes, and 35% due to unexpected additional fees.
- Data Collection: Study a sample of abandoned shopping carts and categorize the reasons for abandonment.
- Hypothesis: The observed distribution of reasons for cart abandonment aligns with the expected distribution.
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Education Funding Allocation:
- Scenario: A school district plans to allocate funds among different subjects (math, science, literature) based on the expected distribution of student interests.
- Data Collection: Survey students to determine their preferred subjects.
- Hypothesis: The observed distribution of student interests in different subjects matches the expected distribution.
- One-Way ANOVA Test
- Two-Way ANOVA Test
- M-ANOVA Test Test
Types of ANOVA Test:-
One-Way ANOVA:- A one-way ANOVA has just one independent variable. For example, difference in Corona cases can be assessed by Country, and Country can have 2, 20, or more different categories to compare.
Two-Way ANOVA:-A two-way ANOVA (are also called factorial ANOVA) refers to an ANOVA using two independent variables. Expanding the example above, a Two-way ANOVA can examine differences in Corona Cases (the dependent variable) by Age group (independent variable 1) and Gender (independent variable 2). Two-way ANOVA can be used to examine the interaction between the two independent variables. Interactions indicate that differences are not uniform across all categories of the independent variables. For example, Old Age Group may have higher Corona cases overall compared to Young Age group, but this difference could be greater (or less) in Asian countries compared to European countries.
M-Way ANOVA(Multivariate ANOVA)- A researcher can also use more than two independent variables, and this is an n-way ANOVA (with n being the number of independent variables you have) aka MANOVA Test. For example, potential differences in Corona cases can be examined by Country, Gender, Age group, Ethnicity, etc, simultaneously. An ANOVA will give you a single (univariate) f-value while a MANOVA will give you a multivariate F value.
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Example: Exam Scores in Different Teaching Methods
- Scenario: Analyzing whether there is a significant difference in exam scores among students taught using three different teaching methods (Method A, Method B, Method C).
- Hypothesis:
- Null Hypothesis (H0): There is no significant difference in exam scores among the teaching methods.
- Alternative Hypothesis (H1): There is a significant difference in exam scores among the teaching methods.
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Example: Impact of Fertilizers on Crop Yield
- Scenario: Investigating whether there is a significant difference in crop yield among fields treated with different types of fertilizers (Fertilizer X, Fertilizer Y, Fertilizer Z).
- Hypothesis:
- Null Hypothesis (H0): There is no significant difference in crop yield among the fertilizers.
- Alternative Hypothesis (H1): There is a significant difference in crop yield among the fertilizers.
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Example: Employee Performance Across Departments
- Scenario: Examining whether there is a significant difference in employee performance scores across different departments in a company.
- Hypothesis:
- Null Hypothesis (H0): There is no significant difference in employee performance across departments.
- Alternative Hypothesis (H1): There is a significant difference in employee performance across departments.
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Example: Effect of Different Diets on Weight Loss
- Scenario: Analyzing whether there is a significant difference in weight loss among individuals following three different diets (Diet A, Diet B, Diet C).
- Hypothesis:
- Null Hypothesis (H0): There is no significant difference in weight loss among the diets.
- Alternative Hypothesis (H1): There is a significant difference in weight loss among the diets.
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Example: Comparison of Customer Satisfaction in Retail Stores
- Scenario: Investigating whether there is a significant difference in customer satisfaction scores among customers visiting three different retail stores (Store X, Store Y, Store Z).
- Hypothesis:
- Null Hypothesis (H0): There is no significant difference in customer satisfaction among the retail stores.
- Alternative Hypothesis (H1): There is a significant difference in customer satisfaction among the retail stores.
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Example: Impact of Drug and Dosage on Recovery Time
- Scenario: Studying whether there is a significant interaction between the type of drug administered (Drug A, Drug B) and dosage level (Low, Medium, High) on recovery time.
- Hypothesis:
- Null Hypothesis (H0): There is no significant interaction between drug type and dosage level on recovery time.
- Alternative Hypothesis (H1): There is a significant interaction between drug type and dosage level on recovery time.
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Example: Influence of Soil Type and Watering Frequency on Plant Growth
- Scenario: Investigating whether there is a significant interaction between soil type (Type 1, Type 2) and watering frequency (Low, Moderate, High) on plant growth.
- Hypothesis:
- Null Hypothesis (H0): There is no significant interaction between soil type and watering frequency on plant growth.
- Alternative Hypothesis (H1): There is a significant interaction between soil type and watering frequency on plant growth.
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Example: Employee Productivity with Respect to Training Methods and Team Size
- Scenario: Analyzing whether there is a significant interaction between different training methods (Method X, Method Y) and team sizes (Small, Medium, Large) on employee productivity.
- Hypothesis:
- Null Hypothesis (H0): There is no significant interaction between training methods and team sizes on employee productivity.
- Alternative Hypothesis (H1): There is a significant interaction between training methods and team sizes on employee productivity.
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Example: Effect of Temperature and Humidity on Energy Consumption
- Scenario: Studying whether there is a significant interaction between temperature levels (Low, Medium, High) and humidity levels (Low, Medium, High) on energy consumption in buildings.
- Hypothesis:
- Null Hypothesis (H0): There is no significant interaction between temperature levels and humidity levels on energy consumption.
- Alternative Hypothesis (H1): There is a significant interaction between temperature levels and humidity levels on energy consumption.
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Example: Impact of Education and Work Experience on Salary
- Scenario: Investigating whether there is a significant interaction between education levels (High School, Bachelor's, Master's) and years of work experience (Low, Medium, High) on salary in a workforce.
- Hypothesis:
- Null Hypothesis (H0): There is no significant interaction between education levels and work experience on salary.
- Alternative Hypothesis (H1): There is a significant interaction between education levels and work experience on salary.
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Example: Impact of Multiple Factors on Product Sales
- Scenario: Studying whether there is a significant interaction between various factors such as advertising strategy, pricing, and location on product sales.
- Hypothesis:
- Null Hypothesis (H0): There is no significant interaction between the considered factors on product sales.
- Alternative Hypothesis (H1): There is a significant interaction between the considered factors on product sales.
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Example: Examining the Joint Effects of Marketing Channels and Product Features on Consumer Preferences
- Scenario: Investigating the joint effects of marketing channels (Online, In-Store) and product features (Feature A, Feature B) on consumer preferences.
- Hypothesis:
- Null Hypothesis (H0): There is no significant interaction between marketing channels and product features on consumer preferences.
- Alternative Hypothesis (H1): There is a significant interaction between marketing channels and product features on consumer preferences.
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Example: Impact of Teaching Methods, Student Engagement, and Classroom Environment on Learning Outcomes
- Scenario: Analyzing the joint effects of teaching methods (Traditional, Blended), student engagement levels (Low, Medium, High), and classroom environment (Standard, Enhanced) on student learning outcomes.
- Hypothesis:
- Null Hypothesis (H0): There is no significant interaction between teaching methods, student engagement, and classroom environment on learning outcomes.
- Alternative Hypothesis (H1): There is a significant interaction between teaching methods, student engagement, and classroom environment on learning outcomes.
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Example: Understanding the Joint Influence of Price, Brand, and Packaging on Consumer Purchase Decisions
- Scenario: Studying the joint influence of price levels (Low, Medium, High), brand reputation (Known, New), and packaging design (Simple,
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N-Way ANOVA Ans: