I am trying to prove that the second half of two part names determines the gender of the whole name in a Romance
language.
I have 30 second parts used only by males in my population and 5 only by
females, with one used by both. It seems that I could reject the nul hypothesis based on 1 vs. 35, but what formula do I use. The books do nor seem to deal with this type of situation.
The answer is not in math, but rather in the criteria of certainity. How certain do you wish your proof to be? 100Percent 90 percent, or 50 percent? Once the certainity is decided, thence you can reject the hypothesis or accept it using any one or more statistical models.
I thought that 95% was most common. My problem is finding statistical models that do not involve means and other nonpertinent functions.
To determine if the second half of a two-part name in a Romance language determines the gender of the whole name, you can perform a hypothesis test using the binomial distribution. The null hypothesis, in this case, would assume that the second half of the name does not determine the gender.
Here's how you can set up the hypothesis test:
1. Define the null hypothesis (H0) and alternative hypothesis (Ha):
- H0: The second half of the name does not determine the gender of the whole name.
- Ha: The second half of the name determines the gender of the whole name.
2. Calculate the expected frequencies:
- Count the total number of names in your population (let's say N).
- Calculate the expected frequency for each gender based on the proportion of names associated with that gender.
- Expected frequency for males = (30 + 1)/N
- Expected frequency for females = (5 + 1)/N
3. Determine the test statistic:
- In this case, we can use the chi-square test statistic.
- Calculate the observed frequencies for each gender based on your data.
4. Set the significance level (α). The typical value is 0.05, but you can choose a different level if necessary.
5. Calculate the chi-square test statistic:
- Calculate the chi-square value using the formula:
X^2 = Σ ((O - E)^2 / E), where O represents the observed frequency and E represents the expected frequency for each category.
- Sum up the values for each gender.
6. Determine the critical value:
- Degrees of freedom (df) = number of categories - 1
- Look up the critical value for the chi-square distribution at the chosen significance level and degree of freedom.
7. Compare the test statistic with the critical value:
- If the test statistic is greater than the critical value, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.
By following these steps, you can calculate the test statistic and compare it with the critical value to determine if there is sufficient evidence to reject the null hypothesis and conclude that the second half of the name determines the gender of the whole name in your population.