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How can you explain the concept of expected frequencies in chi-square tests?

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Understanding the chi-square test begins with grasping the concept of expected frequencies. This statistical method is used to analyze whether there is a significant difference between the expected and observed frequencies in one or more categories. It's particularly useful in fields like genetics, marketing, and social sciences, where you might want to see if the distribution of some variable matches what you would expect by chance. Expected frequencies are essentially the counts you would anticipate in each category if there were no real effect or association, based on probabilities from a theoretical distribution.

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Sakshi Choube

Human Resource | AM Infoweb
Aaditya A. Shrivastava

Analytics and AI-ML Expert | Leading GenAI - LLM (Agentic RAG, Text-to-SQLBOT) | Data Science Leader | NLP/CV | Python…

1 Chi-Square Basics

The chi-square test is grounded in the comparison of what you observe in your data to what you would expect if a particular hypothesis were true. Imagine you're tossing a fair coin; you'd expect an equal number of heads and tails over many tosses. In practice, you compare the actual counts of heads and tails to these expected counts. If the differences are too large, the chi-square test helps you determine if this is likely due to chance or if it suggests an unfair coin.

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Sakshi Choube

Human Resource | AM Infoweb
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Expected frequencies in chi-square tests represent the values anticipated under the assumption of no association between variables. They're calculated based on the null hypothesis, providing a benchmark for comparison with observed frequencies to determine if the variables are independent or not.

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Himakhar Kunchala

Consultant at PwC | Data Analyst | Tech Enthusiast, Nature Lover
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Its more like probability hypothesis which determines chances of getting it right. Supose you ordered a pizza in a very busy place like domino, the chance of getting your pizza under a certain time limit is harder to find out. i hope this helps. Thank you

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??Ali Khreiss??

|Founder @ Bands Consultancy| |Statistician| Data Scientist| |Machine Learning Thesis 2010| |Instructor |Consultant| |Helping 700+ projects| |27K+ Followers|
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The Chi-Square test is one of the non-parametric tests that can help you to determine if there is an independence or dependency between two categorical variables (Nominal or ordinal) if you were testing the relationship which we called the Chi-Square test for independence; while the Chi-Square test for goodness-of-fit uses frequency data from a sample to test hypotheses about the shape or proportions of a population.

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2 Expected Values

To calculate expected frequencies, you need to understand the underlying assumptions. For instance, if you're looking at gender distribution in a population, and you assume it's 50/50 male and female, the expected frequency for each gender in a sample of 100 would be 50. You use these expected values to see if your sample significantly deviates from the assumed distribution, which could indicate an underlying issue or pattern worth investigating.

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3 Calculating Frequencies

To calculate expected frequencies, multiply the total number of observations by the probability of each outcome. If you're observing a categorical variable with multiple levels, like customer preference for three brands, you'd multiply the total number of customers by the proportion expected to prefer each brand. These expected frequencies are crucial for the chi-square test as they are compared against the observed frequencies to see if there's a statistically significant difference.

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Aaditya A. Shrivastava

Analytics and AI-ML Expert | Leading GenAI - LLM (Agentic RAG, Text-to-SQLBOT) | Data Science Leader | NLP/CV | Python | IIIT-Delhi
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?? Understanding expected frequencies in chi-square tests is vital! To calculate, multiply total observations by each outcome's probability. For categorical variables with multiple levels, like customer preferences, multiply total customers by expected proportions for each brand. These expected frequencies are crucial for comparing against observed frequencies to determine statistical significance.

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4 Test Assumptions

Chi-square tests have assumptions that must be met for valid results. Your data should be in frequency form and categories must be mutually exclusive. Each observation should be independent, meaning the selection of one individual doesn't influence another. Expected frequencies should generally be 5 or more to ensure adequate sample size. Violating these assumptions can lead to incorrect conclusions, so it's important to verify them before proceeding.

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??Ali Khreiss??

|Founder @ Bands Consultancy| |Statistician| Data Scientist| |Machine Learning Thesis 2010| |Instructor |Consultant| |Helping 700+ projects| |27K+ Followers|
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The Chi-Square test is a non-parametric test where no parameters regarding the rigidity of populations are required such as mean and standard deviation so the only assumption to detect is that the expected frequency of any item or cell must not be less than 5

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5 Interpretation Tips

Interpreting the results of a chi-square test involves looking at the p-value, which tells you how likely the observed distribution is if the null hypothesis is true. A low p-value suggests that the observed frequencies differ significantly from what was expected. This could indicate a meaningful association between variables or that your initial assumptions about the population distribution might need revising.

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6 Practical Application

In practice, chi-square tests are widely used across various disciplines. For example, in market research, you might want to know if purchase behavior differs by age group. After calculating expected frequencies based on market proportions, you'd use the chi-square test to compare these with actual sales data. If there's a significant difference, it could inform targeted marketing strategies or product development.

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7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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How can you explain the concept of expected frequencies in chi-square tests?

1

2

3

4

5

6

7

1 Chi-Square Basics

2 Expected Values

3 Calculating Frequencies

4 Test Assumptions

5 Interpretation Tips

6 Practical Application

7 Here’s what else to consider

Statistics

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How can you explain the concept of expected frequencies in chi-square tests?

1

2

3

4

5

6

7

1 Chi-Square Basics

2 Expected Values

3 Calculating Frequencies

4 Test Assumptions

5 Interpretation Tips

6 Practical Application

7 Here’s what else to consider

Statistics

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