Question

Quantitative Analysis Exercise

1. Suppose you created an index to measure people’s level of political conservatism (higher score = more conservative). To validate it, you want to compare the mean index scores for people who identify as Republicans vs. Democrats. (This is sort of like what you read about in the article with the love scale; the hypothesis is that Republicans will score higher on the conservatism scale than Democrats.) You find that the Republicans in your sample received scores of {30, 26, 34, 32, 31, 29, 35, 30, 30, 31, 33, 32} and the Democrats in your sample received scores of {16, 23, 20, 17, 20, 22, 24, 19, 17, 21, 22, 22}.

a) Determine the mean score for each group. Create a table below displaying this data. (Don’t forget to include a title!)

b) Use the t-test calculator linked in the slides to generate a p-value for this data.

c) Is the difference between Republicans and Democrats statistically significant?

d) To write up this result, write a paragraph below with the following structure:

1. First sentence should sum up the main relationship (no numbers)

2. Report the two means (answer to “a”)

3. Identify whether the relationship is significant (answer to “c”)

4. Explain what this means in terms of the original research question (here, whether or not the index was valid).

2. Suppose that you wanted to examine racial differences in social media use. You hypothesize black people are more likely to use Twitter than white people. Rather than administer your own survey, you use the already-existing General Social Survey and find the following frequencies:

​White​Black

​Use Twitter​186​47

​Don’t​856​159​

a) To facilitate comparison (and account for the fact that there are more white people than black people in the U.S.), convert the frequencies in the table above to percentages. Round to one place after the decimal. Create a new table below.

b) Identify the main relationship that your table from “a” depicts (using only words, no numbers).

c) Use the chi-square calculator linked in the slides to generate a p-value for this data. (Important: use the frequencies from the original table, not the percentages from “a”)

d) Is the difference between white and black respondents statistically significant?

e) To write up this result, write a paragraph below with the following structure:

1. First sentence should sum up the main relationship (answer to “b”)

2. Report the percentages that describe the main relationship (not all of them). Round to the nearest whole number.

3. Identify whether the relationship is significant (answer to “d”)

4. Identify whether or not the hypothesis has been supported.

Answer 1

Hi, We are supposed to answer one question at a time. Since you have not mentioned which question to answer. I am answering the first one. Please repost the questions that you would like to be answered.

1.

a) Mean score for each group

Step 1: Put the data onto the spreadsheet

Step 2: Mean can be determined using (=average) formula:

b) t score

t score can be calculated using followng formula:

The standard deviation can be calculated using (=stdev.s) command in excel:

df = n1 + n2 -2 = 12 + 12 -2 = 22

By referring to the t distribution table, the p-value at t = 10.72 and df = 22 is 0.0001

c) Since the p value is less than the level of significance, we reject the null hypothesis.

There is a stastically significant difference in the scores of republicans and democrats.

d)

There is enough evidence to claim that the mean score of republicans is more than democrats.

The mean score of Republicans is 31.083 and mean score of democrats is 20.25

There is a significant difference between the republicans and democrats

The researchers hypothesis that republicans have higher scores than democrats is valid.