08. Probabilistic sampling

Module items¶

R Script file code¶

• [[Copy the code]] below ➜ Paste into [[RStudio console]] ➜ Hit Enter

  • source(url("https://raw.githubusercontent.com/ttezcann/ssric-reg/refs/heads/main/docs/assets/attachments/data/0-packages-data.R")); 
    (function(f="08-sampling.R"){if(!file.exists(f)){download.file("https://raw.githubusercontent.com/ttezcann/ssric-reg/refs/heads/main/docs/assets/attachments/modules/08.-probabilistic-sampling/08-sampling.R",f,mode="wb");file.edit(f)}else{download.file("https://raw.githubusercontent.com/ttezcann/ssric-reg/refs/heads/main/docs/assets/attachments/modules/08.-probabilistic-sampling/08-sampling.R",gsub(".R","-original.R",f),mode="wb");file.edit(gsub(".R","-original.R",f))}})()
    

    • When this R script file opens in a new tab, [[Save R script file|save your previous R script file(s)]], and
      • Close the previous tabs (R Script files), which you can find later in the [[Files tab]].

Assignment¶

• Sampling
  • See: [[How to submit an assignment]]

Sample assignment¶

• Sample: Sampling

Suggested reading¶

Learning outcomes¶

1. Learn how to choose and create dataset using
   1. Non-random sample
   2. Simple random sample
   3. Systematic random sample
2. Evaluate a sampling method's representativeness by comparing the sample mean to the population mean against a threshold
3. Identify advantages and disadvantages of different sampling methods

The mission¶

• We will generate four samples and choose one variable.
  • Our variable is family income, coninc.
    • If the mean family income difference between population (GSS data) and samples diverge a lot, if the mean difference is more than $3,000 (the threshold), we can say that sampling method does not represent the population.

• [[Search]] the variable name, conrinc, in Variables in GSS page.

  • Variable name	Variable label	Variable type	Question wording and response categories
    coninc	Respondents' family income	Continuous	What is your family income in dollars? (Min: $281.5; Max, $139,024.4)

    • First, let's create a descriptive table of family income, coninc.

[[Descriptive table]] #code¶

• [[Model code]]

  • 1	descr(gss$variable_here, out = "v", show = "short")

• [[Working code]]

  • 1	descr(gss$coninc, out = "v", show = "short")

    • Line 1: We put coninc here ➜ variable_here.
      • Now, [[find this working code in the R script file]], and
        • [[Highlighting and running|Highlight and run]] the working code in this module's R script file to generate the output shown below, which will appear in the [[viewer tab]] of RStudio.

[[Descriptive table]] #output¶

• Basic descriptive statistics

  • variable	variable label	n	NA.prc	mean	sd
    coninc	Respondents' family income	3563	10.61	47738.65	41328.35

[[Descriptive table]] #interpretation¶

• Descriptive table interpretation sample

  The respondents' family income variable shows that the average family income of the respondents is $47,738, with standard deviation $41,328.

• Descriptive table interpretation template

  The [[variable label]] variable shows the average variable label of the respondents is mean, with standard deviation sd.

• Interpretation explanation

  • After the variable label, we add the word of "variable" in our interpretation:
    • "The respondents' education in years variable shows that..."
  • Depending on the variable, we need to tweak some parts of the interpretation.
    • For example, "the average years of education is...", "the average weeks of working is..." etc.
  • We use the mean (mean column) and standard deviation (sd column) in our interpretation.

The range¶

• So then, if the different samples fall in 50,738 - 44,738 dollars range, we'll assume our sampling methods work.

  • flowchart LR
    A["$44,738"] --- B["$47,738"] --- C["$50,738"]
    
    style A fill:stroke:#333,stroke-width:1px
    style B fill:stroke:#333,stroke-width:5px
    style C fill:stroke:#333,stroke-width:1px

• These are the sampling methods we'll use:

  • flowchart TD
        A("GSS data<br/>3,986 respondents")
    
        B("40% <br/>Non-random sampling<br/>1,594 respondents")
        C("30% <br/>Simple random sampling<br/>1,196 respondents")
        D("20% <br/>Systematic random sampling<br/>798 respondents")
    
        A --> B
        A --> C
        A --> D

[[Non-random sampling]]¶

GSS example 1: 40% non-random sampling¶

• We'll choose 40% of the GSS respondents, but not in a random way. Instead we'll choose the first 40% of them in the dataset in the order they appear, and create a new dataset for them.
  • First, create a new dataset for the first 40% of the GSS respondents.

[[Data creation]] #code for 40% non-random sampling¶

• [[Model code]]

  • 1	new_data_name_here <- head(gss, round(0.40 * nrow(gss)))

• [[Working code]]

  • 1	gssfirst40per <- head(gss, round(0.40 * nrow(gss)))

    • Line 1: We will put gssfirst40per here ➜ new_data_name_here.
      • gssfirst40per is the name of the new dataset, which will appear under gss in Data Environment;
      • head is the order of the selection for the first respondents (tail is for the last);
      • 0.40 is 40%.
        • Now, [[find this working code in the R script file]], and
          • [[Highlighting and running|Highlight and run]] the working code in this module's R script file to create a new data, gssfirst40per.
      • If the codes are correct, the [[viewer tab]] will provide confirmation:
        • 

[[Descriptive table]] #code for 40% non-random sampling¶

• [[Model code]]

  • 1	descr(gssfirst40per$variable_here, out = "v", show = "short")

• [[Working code]]

  • 1	descr(gssfirst40per$coninc, out = "v", show = "short")

    • Line 1: We put coninc here ➜ variable_here. Note that we use gssfirst40per instead of gss.
      • Now, [[find this working code in the R script file]], and
        • [[Highlighting and running|Highlight and run]] the working code in this module's R script file to generate the output shown below, which will appear in the [[viewer tab]] of RStudio.

[[Descriptive table]] #output for 40% non-random sampling¶

• Basic descriptive statistics

  • variable	variable label	n	NA.prc	mean	sd
    coninc	Respondents' family income	1415	11.23	53688.98	44151.37

[[Descriptive table]] #interpretation for 40% non-random sampling¶

• Non-random sampling descriptive table interpretation sample

  The overall respondents' family income mean among GSS respondents is $47,738, while the family income mean with a 40% non-random sample is $53,688.

  In this case since the mean family incomes differ by more than $3,000, we can conclude that these mean family incomes are substantially different.

  • Is a non-random sample preferable method for obtaining generalizable results?

    • It is not preferable; samples that are non-random cannot represent a whole population because all the individuals in the population do not receive equal chances of being selected.
    • Substantially different results were obtained about the family income means because non-random samples are not capable of representing the population as a whole.

• Non-random sampling descriptive table interpretation template

  The overall [[variable label]] mean among GSS respondents is [mean], while the variable label mean with a name of the sampling method name is [mean].

  In this case since the mean variable label differ by more than [threshold], we can conclude that these mean variable label are substantially different.

  OR

  In this case since the variable label do not differ by more than [threshold], we can conclude that these mean variable label are not substantially different.

[[Simple random sampling]]¶

GSS example 2: 30% simple random sampling¶

• We'll choose 30% of the GSS respondents in a random way.
  • First, create a new dataset for the 30% of the GSS respondents that will be chosen randomly.

[[Data creation]] #code for 30% simple random sampling¶

• [[Model code]]

  • 1	new_data_name_here <- gss[sample(nrow(gss), round(0.30 * nrow(gss))), ]

• [[Working code]]

  • 1	gssrandom30per <- gss[sample(nrow(gss), round(0.30 * nrow(gss))), ]

    • Line 1: We will put gssrandom30per here ➜ new_data_name_here.
      • gssrandom30per is the name of the new dataset, which will appear under gss in Data Environment;
      • 0.30 is 30%.
        • Now, [[find this working code in the R script file]], and
          • [[Highlighting and running|Highlight and run]] the working code in this module's R script file to create a new data, gssrandom30per.
      • If the codes are correct, the [[viewer tab]] will provide confirmation:
        • 

[[Descriptive table]] #code for 30% simple random sampling¶

• [[Model code]]

  • 1	descr(gssrandom30per$variable_here, out = "v", show = "short")

• [[Working code]]

  • 1	descr(gssrandom30per$coninc, out = "v", show = "short")

    • Line 1: We put coninc here ➜ variable_here. Note that we use gssrandom30per instead of gss.
      • Now, [[find this working code in the R script file]], and
        • [[Highlighting and running|Highlight and run]] the working code in this module's R script file to generate the output shown below, which will appear in the [[viewer tab]] of RStudio.

[[Descriptive table]] #output for 30% simple random sampling¶

• Basic descriptive statistics

  • variable	variable label	n	NA.prc	mean	sd
    coninc	Respondents' family income	1067	10.79	46641.97	40957.59

[[Descriptive table]] #interpretation for 30% simple random sampling¶

• The overall respondents' family income mean among GSS respondents is 47,738 dollars, and we found 46,641 dollars. This is close! However, when you run those codes, you found a different mean. Also...

  • Here's the issue

    • If you run the data creation code and the descriptive table code again, you will find different results.
      • It's because every single time the data creation code is run, RStudio chooses different 30% of the GSS respondents.
        • There's an inconsistency issue.

  • 30% simple random sampling descriptive table interpretation sample

    The overall family income mean among GSS respondents is $47,738, while the family income mean with a 30% simple random sample is $46,641.

    In this case since the mean family incomes differ by more than $3,000, we can conclude that these mean family incomes are substantially different. In this case since the mean family incomes do not differ by more than $3,000, we can conclude that these mean family incomes are not substantially different.

    • Is a 30% simple random sample preferable to a non-random sample?

      • It is preferable; 30% simple random sampling is better than and superior to non-random sampling as there is a random selection. However, with each time the code is run, there is a different result.
      • Even though this method is better than non-random sampling, there is still inconsistency, as a different 30% of the data is selected each time.

  • 30% simple random sampling descriptive table interpretation template

    The overall [[variable label]] mean among GSS respondents is [mean], while the variable label mean with a name of the sampling method is [mean].

    In this case since the mean variable label differ by more than [threshold], we can conclude that these mean variable label are substantially different.

    OR

    In this case since the variable label do not differ by more than [threshold], we can conclude that these variable label are not substantially different.

[[Systematic random sampling]]¶

GSS example: 20% Systematic random sampling¶

• We'll choose 20% of the GSS respondents in a random way, with assigning the starting point and the choosing interval.
  • First, create a new dataset for the 20% of the GSS respondents that will be chosen randomly and systematically.

[[Data creation]] #code for 20% Systematic random sampling¶

• [[Model code]]

  • 1	new_data_name_here <- gss[seq(4, nrow(gss), 5), ]

• [[Working code]]

  • 1	gss20persystematic <- gss[seq(4, nrow(gss), 5), ]

    • Line 1: We will put gss20persystematic here ➜ new_data_name_here.
      • gss20persystematic is the name of the new dataset, which will appear under gss in Data Environment;
      • 4 is the starting point, so the sample begins with the 4th respondent;
      • 5 means every fifth respondent is selected after that. Because 1 out of every 5 cases is chosen, the sample includes about 20% of the dataset.
        • Now, [[find this working code in the R script file]], and
          • [[Highlighting and running|Highlight and run]] the working code in this module's R script file to create a new data, gss20persystematic.
      • If the codes are correct, the [[viewer tab]] will provide confirmation:
        • 

[[Descriptive table]] #code for 20% Systematic random sampling¶

• [[Model code]]

  • 1	descr(gss20persystematic$variable_here, out = "v", show = "short")

• [[Working code]]

  • 1	descr(gss20persystematic$coninc, out = "v", show = "short")

    • Line 1: We put coninc here ➜ variable_here. Note that we use gss20persystematic instead of gss.
      • Now, [[find this working code in the R script file]], and
        • [[Highlighting and running|Highlight and run]] the working code in this module's R script file to generate the output shown below, which will appear in the [[viewer tab]] of RStudio.

[[Descriptive table]] #output for 20% Systematic random sampling¶

• Basic descriptive statistics

  • variable	variable label	n	NA.prc	mean	sd
    coninc	Respondents' family income	706	11.42	47838.77	41591.10

[[Descriptive table]] #interpretation for 20% Systematic random sampling¶

• The overall respondents' family income mean among GSS respondents is 47,738 dollars, and we found 47,838 dollars. This is extremely close!

  • 20% systematic random sampling descriptive table interpretation sample

    The overall family income mean among GSS respondents is $47,738, while the family income mean with a 20% systematic random sample is $47.838.

    In this case since the mean family incomes do not differ by more than $3,000, we can conclude that these mean family incomes are not substantially different.

    • Is a 20% systematic random sample preferable to a 30% simple random sample?

      • It is preferable; systematic random sampling method provides consistency, and even if there were fewer people used in this sampling, this is better than 30% simple random sampling.

      • Sampling is less about the size of the sample and more about the representativeness of the sample selected.

  • 20% systematic random sampling descriptive table interpretation template

    The overall [[variable label]] mean among GSS respondents is [mean], while the variable label mean with a name of the sampling method is [mean].

    In this case since the mean variable label differ by more than [threshold], we can conclude that these mean variable label are substantially different.

    OR

    In this case since the variable label do not differ by more than [threshold], we can conclude that these variable label are not substantially different.