Chi-squared test: investigating fingerprint types | Wellcome

Summary

This script explores the relationship between fingerprint patterns and gender through a chi-squared test. It explains the process of setting hypotheses, collecting data, calculating expected values, and determining the chi-squared statistic to assess whether there is an association between fingerprint type and sex.

Takeaways

• 👍 Fingerprints are unique to each individual and can be classified into three main patterns: loops, arches, and whorls.
• 🔍 The experiment aims to determine if there is a difference in fingerprint patterns between men and women.
• 🧐 Arches are less common and are grouped with whorls for the purpose of this study.
• 📊 A chi-squared test of association is used to analyze the relationship between two categorical variables, such as sex and fingerprint type.
• ⚖️ The null hypothesis states that sex and fingerprint type are independent, while the alternate hypothesis suggests an association between them.
• 📉 The significance level, typically set at 0.05, determines the strength of evidence required to reject the null hypothesis.
• 📋 Data is organized into a contingency table to facilitate the chi-squared test, with rows for sex categories and columns for fingerprint types.
• 🔢 Expected values in the table are calculated to represent the distribution that would occur by chance if the variables were independent.
• 📘 The chi-squared statistic is computed by comparing observed and expected values, which helps in determining the likelihood of the observed distribution occurring by chance.
• 🔎 A chi-squared table is used to compare the calculated statistic against a critical value to assess the significance of the results.
• 📝 The final step is to decide whether to reject or accept the null hypothesis based on the comparison with the critical value, and to draw a conclusion from the test.

Q & A

What is the purpose of the forensics team dusting for fingerprints at a crime scene?

The purpose is to collect fingerprints because they are unique to each individual, which makes them incredibly useful for determining who has touched what, aiding in solving crimes.

What are the three main types of fingerprint patterns?

The three main types of fingerprint patterns are loops, arches, and whorls.

Why are arches grouped with whorls in this experiment?

Arches are relatively rare, so they are grouped with whorls to simplify the analysis in this experiment.

What is the hypothesis the experiment is testing regarding fingerprint patterns and sex?

The experiment is testing the hypothesis that there might be a difference in the types of fingerprint patterns between men and women.

What is the null hypothesis in the context of this experiment?

The null hypothesis is that knowing someone's sex doesn't tell us anything about how likely they are to have a particular fingerprint type, and vice-versa, meaning the variables are independent.

What is the alternate hypothesis in this experiment?

The alternate hypothesis is that there is an association between fingerprint type and a person's sex, suggesting that men and women tend to have different fingerprint types.

What is the significance of the significance level in a chi-squared test?

The significance level, typically set at 0.05, determines how strong the evidence needs to be before we reject the null hypothesis. If the probability of getting a more extreme result by chance is less than 5%, we reject the null hypothesis.

What is a contingency table and how is it used in the chi-squared test?

A contingency table is a type of table used to display the frequency distribution of the variables. It is used in the chi-squared test to organize observed data and to calculate expected values for each cell to determine if the observed data significantly deviates from what would be expected by chance.

How are expected values in a contingency table calculated?

Expected values are calculated by multiplying the row total by the column total and dividing by the overall total. This gives the theoretical frequency count that would be expected if the variables were independent.

What is the chi-squared statistic and how is it calculated?

The chi-squared statistic is a measure used to determine whether there is a significant association between the variables. It is calculated by summing the squared differences between observed and expected values, each divided by the expected value.

How do you interpret the chi-squared statistic in relation to the degrees of freedom and the critical value?

The chi-squared statistic is compared to a critical value from a chi-squared table based on the degrees of freedom (one less than the number of columns times one less than the number of rows). If the statistic is smaller than the critical value, it suggests that there is not enough evidence to reject the null hypothesis.

What is the conclusion of the experiment based on the chi-squared test result?

Based on the chi-squared statistic being smaller than the critical value, the conclusion is that there is not enough evidence to support an association between fingerprint type and sex, failing to reject the null hypothesis.