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Prospective studies on nutrition

  1. Prospective studies on nutrition often require subjects to keep detailed daily dietary logs. In contrast, retrospective studies often rely on recall. Which method (dietary logs or retrospective recall) do you believe is more likely to achieve accurate results? Explain your response.

  2. We often have a choice of whether to record a given variable on either a quantitative (continuous) or a categorical scale.
    a) How does one measure age quantitatively?
    b) Provide an example by which age can be measured categorically.

  3. Telephone surveys may use a telephone directory to identify individuals for a study. Speculate on the type of household that would be underrepresented by using this sampling frame.

  4. Could the number “0000” appear in a table of random digits? If so, how likely is this?

  5. Body weights of 18 diabetics expressed as a percentage of ideal (defined as body weight divided by ideal body weight x 100) are listed: {107, 119, 99, 114, 120, 104, 88, 114, 124, 116, 101, 121, 152, 100, 125, 114, 95, 117}. Construct a stem-and-leaf plot or box plot of these data and describe the distribution.

  6. Which two measures of central location are equal when data follow a perfectly normal distribution?

  7. To assess the air quality in a surgical suite, the presence of colony-forming spores per cubic meter of air is measured on three successive days. The results are as follows: {12, 24, 30}. Calculate the mean and standard deviation for these data.

  8. In a lottery game, a person must select 5 numbers from a total of 40. Tracy has chosen 7, 8, 9, 10, 11. Jaime has chosen 39, 17, 37, 5, 28. Who has a greater chance of winning?

  9. In a box, there are 8 orange, 7 blue, and 6 red balls. One ball is selected randomly. What is the probability that it is neither orange nor red?

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Sample Answer

 

 

Dietary Logs vs. Retrospective Recall

  • Dietary Logs: More accurate. Subjects record food intake in real-time, minimizing memory bias and forgotten details.
  • Retrospective Recall: Less accurate. Subjects rely on memory, which can be prone to errors in portion sizes, types of food, and timing.

2. Measuring Age

a) Quantitative (Continuous):

  • Measured in years, months, days, or even hours (for newborns).

b) Categorical:

  • Age groups (e.g., infant, child, teenager, adult, senior citizen).
  • Developmental stages (e.g., pre-school, elementary school age).

Full Answer Section

 

 

 

 

3. Telephone Surveys and Sampling Bias

Households underrepresented by using a telephone directory:

  • Those without landlines (increasingly common).
  • Low-income households (less likely to have landlines).
  • Mobile-only households.

4. “0000” in Random Digits Table

  • Yes, “0000” can appear in a table of random digits.
  • Probability depends on the table’s construction. If digits are generated with equal likelihood (0-9), the probability would be 1/10 (one out of ten possible digits).

5. Body Weights and Data Distribution

Option 1: Box Plot (Recommended)

Description:

  • The data appears somewhat skewed to the right (higher weight percentages).
  • The median (middle value) is around 114.
  • The interquartile range (IQR) is from 104 to 121.
  • There are outliers at 88 and 152.

Option 2: Stem-and-Leaf Plot

8 | 8
9 | 5 9
10 | 0 1 4 4 7
11 | 4 4 6 7 9
12 | 0 1 4
15 | 2

Interpretation:

  • Similar to the box plot, the data shows a right skew.
  • Most values fall between 100 and 125.

6. Measures of Central Location in Normal Distribution

  • Mean and Median are equal when data follows a perfectly normal distribution.

7. Air Quality and Descriptive Statistics

  • Mean: (12 + 24 + 30) / 3 = 22 spores per cubic meter
  • Standard Deviation: Calculate the squared deviations from the mean, find the variance (average of squared deviations), and take the square root. However, with only 3 data points, the standard deviation might not be very representative.

8. Lottery Chance

Both Tracy and Jaime have an equal chance of winning (assuming a fair lottery). Each selection has the same probability of being chosen, and their specific number choices don’t influence each other.

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