Conclusion
Let's review each of the tests that we've conducted and the conclusion we've drawn from them.
Correlation:
This test uses scatterplots to analyze the relationship between our two categorical variables: median household income and average math score from PISA exam for each country.
We found that our r-value was moderately strong. Thus, we concluded that there is most likely some kind of relationship between our two factors.
Two Sample T-Test for Means:
We tested our null hypothesis to see if there is a significant difference between the two means from group A and group B. Remember, group A contains the countries that had a higher median income level than group B.
From our conclusion, we found that the means were significantly different. This is because we received a p-value smaller than our significance value. This tells us that the t-statistic we received was very rare. Rare enough that the means were noticeably different from each other.
Chi-Squared Test of Independence:
Our goal was to find out if median household income and the math score on the PISA test are independent of each other. By conducting this test, we found that our p-value was much smaller than our significance level. Thus, we can reject the null hypothesis and conclude that the two variables are dependent on each other.
*Remember, it is not allowed in statistics to conclude that one factor causes another. Instead, we state that they are related and that their relationship is strong.
While there are many ways to interpret data we are given, this was just one small example. We could conclude that two seemingly random variables do indeed have some relationship. However, what can we do now that we know that median household income and average math test scores are related? This gives us some insight into why some countries do better than others. However, we must be careful to not conclude that median income is the only factor affecting the math score. There are many other variables that must be taken into account such as an individual student's ability in math, the teachers' skill set, a country's education department, and many more.
To view the works cited page, click here.
Correlation:
This test uses scatterplots to analyze the relationship between our two categorical variables: median household income and average math score from PISA exam for each country.
We found that our r-value was moderately strong. Thus, we concluded that there is most likely some kind of relationship between our two factors.
Two Sample T-Test for Means:
We tested our null hypothesis to see if there is a significant difference between the two means from group A and group B. Remember, group A contains the countries that had a higher median income level than group B.
From our conclusion, we found that the means were significantly different. This is because we received a p-value smaller than our significance value. This tells us that the t-statistic we received was very rare. Rare enough that the means were noticeably different from each other.
Chi-Squared Test of Independence:
Our goal was to find out if median household income and the math score on the PISA test are independent of each other. By conducting this test, we found that our p-value was much smaller than our significance level. Thus, we can reject the null hypothesis and conclude that the two variables are dependent on each other.
*Remember, it is not allowed in statistics to conclude that one factor causes another. Instead, we state that they are related and that their relationship is strong.
While there are many ways to interpret data we are given, this was just one small example. We could conclude that two seemingly random variables do indeed have some relationship. However, what can we do now that we know that median household income and average math test scores are related? This gives us some insight into why some countries do better than others. However, we must be careful to not conclude that median income is the only factor affecting the math score. There are many other variables that must be taken into account such as an individual student's ability in math, the teachers' skill set, a country's education department, and many more.
To view the works cited page, click here.