Hand Calculations

  1. Two-way frequency table is below. 
    2.     VAR1
VAR2 A B C
   x 5 3 6
   y 6 5 3
  2. Row Percentages Table 
    3.     VAR1
VAR2     A     B     C   Sum
   x  35.7  21.4  42.9 100.0
   y  42.9  35.7  21.4 100.0
  3. Column Percentages Table 
    4.      VAR1
VAR2      A     B     C
  x    45.5  37.5  66.7
  y    54.5  62.5  33.3
  Sum 100.0 100.0 100.0
  4. Total Percentages Table 
    5.      VAR1
VAR2      A     B     C   Sum
  x    17.9  10.7  21.4  50.0
  y    21.4  17.9  10.7  50.0
  Sum  39.3  28.6  32.1 100.0
Note:
  • In the remaining questions, the “trick” to making the computation is to determine if the question is restricted to only a portion of the data. If the question is restricted to one of the levels that corresponds to a row then compute a row percentage (i.e., divide the raw frequency by the total of its row). If the question is restricted to one of the levels that corresponds to a column then compute a column percentage (i.e., divide the raw frequency by the total of its column). If the question does not restrict to a level in either a row or column, then compute a table or total percentage (i.e., divide the raw frequency by the total number of individuals in the table.
  • Generally speaking, percentages should be rounded to one decimal place (as illustrated below).

Fire Blight Disease

  1. The response variable is the outcome (i.e., time of death of the tree).
  2. The percentage of all trees in the control treatment that were dead within the first year is \(\frac{5}{7}\times 100\) = 71.4%.
  3. The percentage of ALL trees that were in the control treatment AND were dead within the first year is \(\frac{5}{24}\times 100\) = 20.8%.
  4. The percentage of the trees in the control treatment that died after four years is \(\frac{0}{7}\times 100\) = 0.0%.
  5. The percentage of the trees that died after 2-4 years that were in the control treatment is \(\frac{2}{9}\times 100\) = 22.2%.
  6. The percentage of all trees that were dead within the first year is \(\frac{10}{24}\times 100\) = 41.6%.
  7. Trees died much earlier when no action was taken (Table 1). Spraying and removing branches was slightly more effective (i.e., trees lived longer) than just removing branches.

Table 1: Percentages of outcomes within each tree treatment type.

                     out
treat                 Within 1 Year 2-4 Years Later 4+ Years Later   Sum
  No Action (control)          71.4            28.6            0.0 100.0
  Removed Branches             37.5            37.5           25.0 100.0
  Sprayed and Removed          22.2            44.4           33.3  99.9

Religion and Genetic Counseling

  1. The percentage of Jewish physicians that support genetic counseling was \(\frac{21}{47}\times100\)= 44.7%.
  2. The percentage of Catholic physicians that don’t support genetic counseling was \(\frac{52}{62}\times100\)= 83.9%.
  3. The percentage of all physicians surveyed that were Protestant was \(\frac{178}{287}\times100\)= 62.0%.
  4. The percentage of those physicians not supporting genetic counseling that were Catholic was \(\frac{52}{220}\times100\)= 23.6%.
  5. The percentage of all physicians that supported genetic counseling was \(\frac{67}{287}\times100\)= 23.3%.
  6. Respondents that identified as Jewish were more than twice as likely to support genetic counseling than those that identified as Protestant or Catholic (Table 4). Those that identified as Catholic were slightly less supportive than those that identified as Protestant.

Table 4: Row percentages table for level of support of genetic counseling by religion.

           Support Don’t Support Sum
Jewish        44.7          55.3 100
Protestant    20.2          79.8 100
Catholic      16.1          83.9 100