# Interpreting Tables

I need help interpreting these tables. I have started on them but I do no think they are correct. The solutions would be very helpful for my studies.

Problem 1.

Below is a tabulation of the demographic data from the Frequency distribution of a survey done by Ms. Sandra Jones. Her sample consisted of 148 of a total of 3,700 clerical employees in three service organizations.

Based on the tabulation provided below, describe the sample characteristics.

Table 1: Frequency Distributions of Sample (n = 148)

RACE EDUCATION GENDER

Non-whites = 48 (32%) High School = 38 (26%) Males =111(75%)

Whites = 100 (68%) College Degree = 74 (50%) Females = 37 (25%)

Masters Degree = 36 (24%)

AGE # OF YEARS IN ORG. MARITAL STATUS

< 20 = 10(7%) < 1 year = 5 (3%) Single 20 (14%)

20-30 = 20(14%) 1-3 = 25(17%) Married 108 (73%)

31-40 = 30(20%) 4-10 = 98(66%) Divorced 13 (9%)

>40 = 88(59%) >10 = 20(14%) Alternative Lifestyle 7 (4%)

Here is another tabulation of the Means, Standard Deviations, etc., for Ms. Jones' data.

How would you interpret these data?

Table 2 and 3 are in the word doc, refer to the doc.

This is what I came up with but not sure if it's correct.

Table 1 - Description of the sample characteristics

The race of employees based on the sample are majority white at 68% and non-whites at 32%. The education level is that half of the employees have a college education, 24% of the employees have a master degree and 24% of the employees have a high school degree. The majority of the employees are male at 75% and 25% of the employees are female. The majority of the age of employees are greater than 40 years of age at 59%, 7% less than 20 years of age, 14% between 20 - 30 and 20% between 31 - 40 years of age. Most employees (66%) have worked at the organization from 4-10 years, 17% have worked there 1-3 years, 14% have worked there more than 10 years and 3% have worked there less than a year. The marital status where most employees are married at 73%, 14% of employees are single, 9% are divorced and 4% lead an alternative lifestyle.

Table 2 - Interpretation

Table 2 gives you the average (mean) for each of the variables as well as the standard deviation (average spread of sample data about the mean) and the range (minimum to maximum) for the sample data points. This gives you an idea of the employees in the sample, their average age, average number of years married, average stress, job involvement and performance. This tells you if the sample is similar or different employees are from each other. The average age of employees are 37.5 and the average number of years married for employees is 12.1 years. There's a wide variation in the number of years married (standard deviation = 24) indicating ???

Table 3 - Interpretation

In Table B the variables are correlated with each other. This means that you are seeing if they "move together" closely (strong relationship) or loosely (modest relationship) or not at all (no relationship). It shows that there is a strong relationship between age and number of years married and a loose relationship with the other three variables, stress, job involvement and performance.

Age the dependent variable does not have a highly significantly positive correlation to the four independent variables, numbers of years married, stress, job involvement and performance. This makes sense since age is not a factor in job performance.

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Here is another tabulation of the Means, Standard Deviations, etc., for Ms. Jones' data.

How would you interpret these data?

Table 2: Means, Standard Deviations and Other Statistics

VARIABLE MEAN STD. DEV MODE MIN MAX

Age 37.5 18 38 20 64

# of Years Married 12.1 24 15 0 32

Stress 3.7 1.79 3 1 5

Job Involvement 3.9 1.63 4 2 5

Performance 3.6 0.86 3 3 5

From the same research done by Ms. Jones, the following inter-correlation matrix is shown. Interpret these results.

In the age group, there are many people at age of 38. The youngest is 20 and the oldest is 64. Further, all these ages locate within two standard deviations away from the mean. In other ways, there may be no obvious outlier in this data set.

For the number of years married, there ...

#### Solution Summary

The expert examines interpreting tables.

Fixed model - Robust Regression Interpretation of results

Question One:

This problem employs a dataset on labor markets in 23 OECD countries for the years 1980 to 1998.

The variables used in the analysis (followed by descriptive statistics) are:

1. Productivity index [prod] = An index measuring country i's economic output (GDP) per hour worked in year t, normalized such that each country's index = 100 in 1995.

2. Unemployment rate [unr] = The total number of unemployed workers in country i and year t divided by the total number of labor force participants in that country and year, multiplied by 100.

3. Union density [ud] = The ratio of total reported union members (minus retired and unemployed members) in country i and year t to the total number of employees earning wages or salaries in that country and year, multiplied by 100.

4. Public sector growth [gempl] = The one-year percentage growth (from year t-1 to year t) in public sector employment in country i (measured as a proportion, 0 to 1).

5. USD exchange rate growth [usd]: The one-year percentage growth (from year t-1 to year t) in the value of country i's currency relative to the US dollar (measured as a proportion, 0 to 1).

6. Labor force (1K) [lf]: The total number of labor force participants in country i and year t, in thousands.

(See attached)

1. While there are no missing years in the dataset, there are missing observations for some of the variables.

a. If there were no missing values for any variables, how many observations (country-years) would there be for every variable in the summary table of descriptive statistics presented above?

b. Given the number of observations for each variable shown in the summary table, knowing there are no missing years in the data, and knowing that Stata regression drops a case when there are any missing values for any variable for a given country in a given year, what is the maximum number of countries that can be used in a regression analysis (assuming nothing is done to replace missing values)?

c. Given that there are 19 years of data in the regression analyses presented in Table 1, how many countries were used in the analyses?

d. Could we estimate the effect of usd on prod with FE if the value of every country's currency (relative to the US dollar) remained the same over the sample time period? Why or why not? Please answer in 2-3 sentences.

2. Write the general equations for the specifications in columns (1) and (2). Use lowercase b for the regression coefficients and, where appropriate, a to indicate fixed effects and/or T to indicate time effects. Use the variable names presented in brackets [ ] on the prior page, and use subscripts as appropriate. You do not have to include an error term.

Column 1:

Column 2:

3. Using the models estimated without time effects, interpret:

A. The effect of a 5-percentage-point increase in union density.

B. The effect of a 10-percent increase in the growth of the public sector.

4. Compare the specifications with time effects to those without time effects. What do the differences in the statistically significant coefficients imply about the time effects? Note that the time effects are jointly statistically significant with a p-value of 0.00. Please answer in 2-3 sentences.

Question Two:

Table 2 presents results of a study of the effect of differences in the fraction of new immigrants on crime rates in U.S. metropolitan area (MA's) over nine years.

^

a. Write the general equation for the regression in column 2. Use β for the regression coefficients (not the actual numbers in column 2), use the variable names presented in the table in brackets [ ], and use subscripts as appropriate. If appropriate, use MA and T as fixed effects.

b. Using the results in column 2:

i. Ignoring significance, what is the effect of a twenty (20 percentage point or .2 fraction) increase in new immigrants on the overall crime rate?

ii. Form a 95% confidence interval around the effect you've just calculated.

c. Two parts:

i. In what two ways does the coefficient on Fraction of new immigrants [IMM] differ between columns 1 and 2?

ii. Why does it differ and what does this indicate about the estimates in columns 1 and 2?

d. Using the results in column 2: For an MA with 10% (.10 fraction) Hispanic population, what is the effect of a one percentage point (.01 fraction) increase in the percent female on the metropolitan crime rate?

e. Using the results in column 2, what is the effect of a one percent increase in population of an MA on the overall crime rate of the MA?

f. Two parts:

i. What hypotheses do the p values for F's in column 2 at the bottom of the table test? (Hint: There are two different p values (F's) and thus two different hypotheses.)

ii. What do you conclude from the tests?

Table 2

Regression coefficients: Log metropolitan area (MA) overall crime rate (CR) on various variables

(See attached)

Source: Calculations from Current Population Surveys (CPSs) and Uniform Crime Reports (UCR)

Notes: Robust Standard errors are parentheses and constant included but not shown.

~ p-value from an F-test

z: "Fraction" varies from 0 to 1 and differs in measurement from percent, which varies from 1 to 100.