Part 1

1.

Probability sampling is a method where every member of a population has a known, non-zero chance of being selected, usually through a random selection process. This approach is highly effective for creating a sample that accurately represents the population, reducing bias and allowing for reliable generalizations from the sample to the population.

Non-probability sampling, on the other hand, involves selecting samples based on subjective judgment rather than random selection, meaning not everyone in the population has a chance of being included. This method is quicker and less costly but often leads to bias, making it difficult to generalize findings to the broader population.

The choice between different probability sampling methods depends on the specific needs. If we’re looking for simplicity and have a well-defined and accessible population, simple random sampling is straightforward and effective. For populations that are more diverse or segmented, we might consider stratified sampling to ensure all segments are proportionally represented in the sample.

2.

Probability Sampling Designs

  • Simple Random Sampling: Every member of the target population has an equal chance of being selected, much like names drawn from a hat. This method aims to eliminate bias, ensuring that the sample accurately represents the larger group. However, it can be challenging and costly to implement effectively, especially with large populations.

  • Stratified Random Sampling: This involves dividing the population into smaller groups or strata based on shared characteristics (like age or income) and then randomly sampling from each stratum. This ensures all segments of the population are represented in the sample, enhancing the accuracy of results that reflect the entire group.

Non-Probability Sampling Designs

  • Purposive Sampling: This technique involves selecting participants based on specific purposes relevant to the research question. Researchers use their judgment to choose individuals who are particularly knowledgeable or experienced with the subject matter. While this method can provide in-depth and detailed data from a target demographic, it does not necessarily produce results that are generalizable to the entire population, as the sample is not randomly selected.

  • Quota Sampling: Researchers identify segments of the population of interest and then non-randomly select participants to meet predefined quotas that reflect the demographics of the whole population. This method can quickly gather a diverse sample but lacks the randomness of probability methods, which may affect the generalizability of the results.

Part 2.

1.

The population of interest in the CPS primarily targets the U.S. civilian noninstitutional population aged 16 years and older. This includes individuals who are not in institutions such as prisons, long-term care hospitals, or nursing homes, and who are not on active duty in the Armed Forces. The survey covers various demographic segments across the entire United States, without any restrictions based on occupation.

2.

CPS uses a sample of about 60,000 eligible households to estimate population parameters like the unemployment rate and the employment-to-population ratio. These households are selected to reflect the entire U.S. civilian noninstitutional population aged 16 years and over.

A unique aspect of the CPS methodology is its use of a dual approach for data collection, which includes both a household survey for labor force data and an establishment survey for employment data. This dual approach allows the CPS to capture a comprehensive range of labor market dynamics from both household and business perspectives. The household survey’s broad scope includes self-employed individuals, unpaid family workers, agricultural workers, and private household workers, which are typically excluded from the establishment surveys.

Additionally, the CPS adjusts its data for seasonal variations, using concurrent seasonal adjustment methodology. This involves recalculating seasonal factors each month using all available data, including the current month’s, which helps to provide a clearer picture of underlying economic trends without seasonal distortions.

3.

Yes, CPS is designed to be a representative sample of the entire U.S. civilian noninstitutional population aged 16 years and over. Its sampling methodology and careful design ensure that it accurately reflects the demographic and labor force characteristics of this population across the United States.

The CPS uses a stratified sampling technique, which means the country is divided into various strata or segments that are representative of geographical, demographic, and possibly other characteristics. This allows the survey to cover all states and demographic groups appropriately, ensuring diversity and representativeness in the sample. Additionally, the sample size of about 60,000 households each month is sufficiently large to provide reliable estimates with a reasonable margin of error for national labor market indicators.

Moreover, the CPS methodology includes regular updates and recalibrations, such as the introduction of new population controls annually, which helps maintain its accuracy and relevance over time. Seasonal adjustments further refine the data, allowing analysts to observe underlying economic trends more clearly by filtering out regular seasonal fluctuations.

6.

head(cps_data)
##   YEAR SERIAL MONTH HWTFINL       CPSID ASECFLAG ASECWTH PERNUM WTFINL
## 1 2019      4     3      NA 2.01803e+13        1 2031.67      1     NA
## 2 2019      6     3      NA 2.01903e+13        1 1232.04      1     NA
## 3 2019      7     3      NA 2.01903e+13        1 1209.17      1     NA
## 4 2019      8     3      NA 2.01903e+13        1 1146.23      1     NA
## 5 2019      8     3      NA 2.01903e+13        1 1146.23      2     NA
## 6 2019     13     3      NA 2.01902e+13        1 1587.98      1     NA
##        CPSIDP      CPSIDV  ASECWT LABFORCE INCWAGE
## 1 2.01803e+13 2.01803e+14 2031.67        2   18000
## 2 2.01903e+13 2.01903e+14 1232.04        1       0
## 3 2.01903e+13 2.01903e+14 1209.17        2   12000
## 4 2.01903e+13 2.01903e+14 1146.23        1       0
## 5 2.01903e+13 2.01903e+14 1480.79        2   12000
## 6 2.01902e+13 2.01902e+14 1587.98        1       0
summary(cps_data)
##       YEAR          SERIAL          MONTH           HWTFINL      
##  Min.   :2019   Min.   :    1   Min.   : 1.000   Min.   :    0   
##  1st Qu.:2021   1st Qu.:17983   1st Qu.: 3.000   1st Qu.: 1575   
##  Median :2022   Median :35715   Median : 5.000   Median : 3404   
##  Mean   :2022   Mean   :36370   Mean   : 5.665   Mean   : 3120   
##  3rd Qu.:2023   3rd Qu.:54110   3rd Qu.: 9.000   3rd Qu.: 4330   
##  Max.   :2024   Max.   :94633   Max.   :12.000   Max.   :20133   
##                                                  NA's   :800468  
##      CPSID              ASECFLAG          ASECWTH            PERNUM      
##  Min.   :0.000e+00   Min.   :1         Min.   :  110     Min.   : 1.000  
##  1st Qu.:2.020e+13   1st Qu.:1         1st Qu.:  998     1st Qu.: 1.000  
##  Median :2.021e+13   Median :1         Median : 1923     Median : 2.000  
##  Mean   :1.904e+13   Mean   :1         Mean   : 1982     Mean   : 2.121  
##  3rd Qu.:2.022e+13   3rd Qu.:2         3rd Qu.: 2627     3rd Qu.: 3.000  
##  Max.   :2.024e+13   Max.   :2         Max.   :10925     Max.   :16.000  
##                      NA's   :3592239   NA's   :3896454                   
##      WTFINL           CPSIDP              CPSIDV              ASECWT       
##  Min.   :    0    Min.   :0.000e+00   Min.   :0.000e+00   Min.   :   86    
##  1st Qu.: 1581    1st Qu.:2.020e+13   1st Qu.:2.020e+14   1st Qu.: 1018    
##  Median : 3402    Median :2.021e+13   Median :2.021e+14   Median : 1951    
##  Mean   : 3200    Mean   :1.904e+13   Mean   :1.904e+14   Mean   : 2048    
##  3rd Qu.: 4422    3rd Qu.:2.022e+13   3rd Qu.:2.022e+14   3rd Qu.: 2749    
##  Max.   :44748    Max.   :2.024e+13   Max.   :2.024e+14   Max.   :17422    
##  NA's   :800468                                           NA's   :3896454  
##     LABFORCE        INCWAGE        
##  Min.   :0.000   Min.   :       0  
##  1st Qu.:1.000   1st Qu.:       0  
##  Median :1.000   Median :   33280  
##  Mean   :1.308   Mean   :20957460  
##  3rd Qu.:2.000   3rd Qu.:  125000  
##  Max.   :2.000   Max.   :99999999  
##                  NA's   :3896454
# Summarize income
aggregate(INCWAGE ~ LABFORCE, data = cps_data, FUN = mean)
##   LABFORCE      INCWAGE
## 1        0 98397547.484
## 2        1     2387.757
## 3        2    56369.476
# Label LABFORCE
cps_data$LABFORCE <- factor(cps_data$LABFORCE,
                            levels = c(0, 1, 2),
                            labels = c("Not in Labor Force", "Unemployed", "Employed"))

# Plot
boxplot(cps_data$INCWAGE ~ cps_data$LABFORCE,
        main = "Income by Labor Force Status",
        xlab = "Labor Force Status",
        ylab = "Income",
        col = c("gray", "red", "blue"))

legend("topright",
       legend = levels(cps_data$LABFORCE),
       fill = c("gray", "red", "blue"),
       title = "Labor Force Status")

The plot and summary table indicate that individuals not in the labor force have reported a wide range of incomes. This group is diverse, including retirees, students, and possibly individuals living off investments, which could account for the variance.

On the other hand, the unemployed group shows a markedly lower average income level. This is consistent with the expectation that unemployed individuals would generally have lower incomes, reflecting unemployment benefits or occasional part-time work, rather than regular full-time wages.

The employed group displays higher income levels compared to the unemployed, aligning with the fact that these individuals are actively earning wages from employment. The reported income for this group appears to be a typical wage figure, suggesting a steady source of income from consistent employment.