One political science student decided to compare GDP per capita in free and not free countries (in the Freedom House notation). He wants to prove that the mean value of GDP per capita differs in these two types of states.
1.1. What is the null hypothesis in this research?
1.2. What can be considered as the Type I error in this research?
1.3. What can be considered as the Type II error in this research?
The student chose 90 countries, performed t-test and got the p-value of 0.015.
1.4. Interpret the p-value in the context of this study.
1.5. What conclusion should be made at the 5% significance level?
1.6. Considering the conclusion in 1.4, what error, Type I or Type II, might the student make?
Imagine the following situation. A student has to compare the average salary of graduates who completed a bachelor degree in different fields: Art & Design, Business & Economics, Computer Science, Humanities, Mathematics, and Social Sciences. To do this he decided to perform multiple t-tests (one test for each pair of fields).
2.1. Is it a good idea or not? Explain your answer.
2.2. If it is not a good idea, suggest a better solution for this problem.
A researcher wants to check whether the level of government effectiveness is different in states with various origins of the legal system. To conduct the analysis he compares the average value of the Government Effectives Index (from World Government Indicators database) in countries with different legal systems: Anglo-Saxon, Continental, and Soviet. Below there are two R outputs.
The output A represents the results of performing multiple t-tests with no corrections. A researcher performed t-tests for every pair of legal origins (one t-test per pair) and got corresponding p-values. For example, while comparing the mean value of Government Effectiveness Index in states with Anglo-Saxon system and Continental system, he got the p-value of 0.275.
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## Pairwise comparisons using t tests with pooled SD
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## data: df$govef and df$LegOrigin
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## Anglo-Saxon Continental
## Continental 0.275 -
## Soviet 0.127 0.019
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## P value adjustment method: noneThe output B shows the results of performing multiple t-tests using the Bonferroni correction. Again the t-tests are done for each pair of legal origins, but now the p-values are adjusted according to the correction.
##
## Pairwise comparisons using t tests with pooled SD
##
## data: df$govef and df$LegOrigin
##
## Anglo-Saxon Continental
## Continental 0.826 -
## Soviet 0.380 0.057
##
## P value adjustment method: bonferroniHow does the difference in the results presented in the outputs A and B correspond to the logic of using the Bonferroni correction in multiple comparisons?
You have the dataset (pt-dataset.csv) on some political indicators for different countries. It contains only the small share of indices that were used by T.Persson and G.Tabellini in their profound research on the economic effects of constitutions.
The indicators include:
Governance & Corruption Index (gac). It ranges from 0 to 10, and lower values correspond to the lower level of corruption perceived.
Government Effectiveness Index (govef). It ranges from 0 to 10, and lower values correspond to higher effectiveness.
Gastil index (gastil). Average of indices for civil liberties and political rights developed by Freedom House. It ranges from 1 to 7, and lower values correspond to more freedom in countries.
Gini index on income distribution (gini). The average social inequality index of two points: the observation closest to the 1980 and the observation closest to the 1990.
Also this dataset contains the variable LegOrigin which is the origin of the legal system in a country: Anglo-Saxon, Continental, and Soviet.
Choose one indicator from the list above and compare its mean values in states with different legal system origin (there are 3 groups of states: with Anglo-Saxon, Continental, and Soviet legal system). Use the analysis of variance for this task.
4.1. Indicate the index you chose for your analysis.
4.2. Formulate the null hypothesis you are going to test.
4.3. Formulate the alternative hypothesis.
4.4. Run commands in R so as to test your null hypothesis. Provide the code you use to do it.
4.5. Interpret the output you get. Remember that your interpretation should include the correct statistical explanation as well as the substantial conclusions.