What Is Fisher's Exact Test and How Is It Used?

TL;DR

Fisher's Exact Test determines if a sample's distribution significantly deviates from an expected distribution, such as the color ratio in a bag of M&Ms. By calculating probabilities for specific outcomes and combining them, this test generates a p-value to assess uniqueness, helping in enrichment analysis across various datasets.

Transcript

hello and welcome to a stat quickie today we're going to talk about Fisher's exact test and enrichment analysis but first let's eat some M&Ms I want to share some with my friends so I just take one handful and get seven blue and one red what does this say about the distribution of colors in the bag do I have more blues than normal lastly can I calc... Read More

Key Insights

• 🏆 Fisher's exact test is a statistical method used to analyze categorical data and determine if a sample is significantly different from an expected distribution.
• 🏆 Probability calculations are crucial in Fisher's exact test to assess the likelihood of obtaining a specific sample.
• 🎴 P-values play a key role in determining the significance of a sample in Fisher's exact test, with lower values indicating greater uniqueness.
• 😫 Enrichment analysis can be performed using Fisher's exact test to identify overrepresented categories within a sample set.
• 🍵 The process of calculating probabilities and p-values can be computationally intensive, but computers can efficiently handle the calculations.
• 🍹 The p-value in Fisher's exact test represents the sum of the probabilities of all equally rare or rarer outcomes, providing a measure of the sample's uniqueness.
• 👂 Fisher's exact test can be applied beyond M&Ms to analyze various datasets, such as gene lists for enrichment analysis.

Questions & Answers

Q: How is Fisher's exact test applied to the distribution of M&Ms in a sample?

Fisher's exact test is used to determine if a sample, like a handful of M&Ms, is significantly different from an expected distribution. By calculating probabilities, one can assess the uniqueness of the sample.

Q: How are probabilities calculated to determine the likelihood of getting a specific sequence of M&M colors?

Probabilities for getting a specific sequence of M&M colors, like seven blue and one red, are computed by considering the decreasing numbers of each color in the bag for each successive draw. These individual probabilities are then multiplied to get the probability of the specific sequence.

Q: What is the significance of the p-value in Fisher's exact test?

The p-value in Fisher's exact test indicates the probability of obtaining a sample as extreme as the observed sample. It is calculated by summing up the probabilities of all equally rare or rarer outcomes, providing a measure of the sample's uniqueness.

Q: How does one perform enrichment analysis using Fisher's exact test?

Enrichment analysis using Fisher's exact test involves comparing a sample set, such as a list of genes, to an expected distribution to assess if certain categories are overrepresented. The same principles of probability calculation and p-value determination apply.

Summary & Key Takeaways

• Using M&Ms, the content explains Fisher's exact test and enrichment analysis.

• Probability calculations are detailed to determine if a sample is unique.

• The process of calculating p-values and determining if a sample is special is demonstrated.