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  3. Inference for Categorical Data in R

Exercise

SE with less data

The less data that you have to make an estimate, the more uncertainty you will have in that estimate. This is reflected in the standard error. In this exercise you'll develop a feel for this relationship by looking at datasets of different sizes.

Two new smaller datasets have been created for you from gss2016: gss2016_small, which contains 50 observations, and gss2016_smaller which contains just 10 observations.

Instructions 1/4

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  • 1
    • Using this gss2016_small, create a bootstrap distribution called boot_dist_small using the familiar steps:
    • specify that you're interested in the consci variable where success is indicated by having "High" confidence.
    • generate 500 bootstrap replicates.
    • calculate the proportion for each.
  • 2

    Summarize the boot_dist_small's SE with its standard deviation then pull it out and save it to SE_small_n.

  • 3
    • Repeat this process of generating the bootstrap distribution for gss2016_smaller and save it to boot_dist_smaller. Save yourself some time by copying and pasting the previous code block and swapping the dataset name.
  • 4
    • Repeat this process of extracting the SE of boot_dist_smaller and save it to SE_smaller_n. Copy and paste comes in handy here again.
    • Run the code to compare the two SEs and their respective sample sizes. How does sample size affect standard error?