Analysis of a Single Variable (Exam 1)

Question 1

what are the 4 steps in a statistical analysis?

Answer 1

1) identify a population of interest and a question about that population
2) collect sample data from the population
3) perform preliminary data analysis to summarize data (descriptive statistics)
4) draw conclusions from data (inferential statistics)

Question 2

distribution

Answer 2

• tells us what values it takes and how often it takes those values
• ways of describing a variable’s distribution (graphically/numerically) from a sample depend on the variable type (categorical/quantitative)

Question 3

categorical variables

Answer 3

variables that put the individual into one of several groups/categories

Question 4

distribution of a categorical variable

Answer 4

• lists the categories and gives either the count or percentage of individuals who fall in each category
• 2 methods:
• pie chart, bar graph

Question 5

pie chart

Answer 5

• shows how a whole group (the variable) is subdivided into smaller groups (categories)
• the size of the slice is proportional to the fraction of the sample/population in that category
• the sum of the %’s shown by each slice must add up to 100% (every individual must be represented, uses an “other” category)

Question 6

bar graph

Answer 6

• represents each category as a bar
  The height of the bar shows the category count%
• don’t have to plot every individual in the sample
• to transform it into a pie chart, we’d have to know the “other” category to make it add up to 100%
• has space between each bar because the categories aren’t in order or directly adjacent to each other

Question 7

distribution of a quantitative variable

Answer 7

• tells us what values the variable takes and how often it takes these values
• 4 methods:
• histogram, stemplot, boxplot, time plot

Question 8

quantitative variables

Answer 8

variables that take values for which arithmetic operations make sense

Question 9

histogram

Answer 9

• a graph of the distribution of a quantitative variable whose values are grouped together
• take the full range and divide it up
• bars are directly adjacent to each other (touch), “classes” are all close to each other, and ordered
• nobody is excluded

Question 10

stemplot

Answer 10

• “sideways” histogram that shows the actual numbers of the distribution
• stem: consists of all but the final digit
• leaf: the final digit
• good for small datasets (<40-50)
• unlike histograms, stemplots show the actual values of the data
• less flexible than histograms

Question 11

shape

Answer 11

• symmetric distribution: the right & left sides of the histogram are approx mirror images of each other
• skewed to the right: the right side of the histogram extends much further out than the left
• skewed to the left: the left side of the histogram extends much further out than the right
• unimodal: 1 peak
• bimodal: 2 peaks
• multimodal: multiple peaks

Question 12

center

Answer 12

• where is the middle?
• mean: average of all observations of the variable, but highly influenced by outliers & extreme data values (preferred unless the distribution is strongly skewed/presents outliers)
• median: resistant to outliers & extreme values, midpoint (50th percentile) of the distribution of the variable

Question 13

spread

Answer 13

• what is the variability of the data from the center?

these are not resistant to outliers…
- variance: measures the dispersion (spread about the mean) of all the observations
- standard deviation: the square root of the variance, indicates the extent of deviation for a group as a whole

these are better to describe the spread when the data is strongly skewed/present outliers…
- 5-number summary (percentiles): min, Q1, median, Q3, max
- interquartile range (IQR): Q3 – Q1, can be used to identify outliers

Question 14

boxplot

Answer 14

• graphical rendition of statistical data based on the min, Q1, median, Q3, max
• the info in the 5-number summary can be graphically displayed in a boxplot
• central box spans Q1 & Q3
• line marks the median within the central box
• lines extend from the box to mark the min & max
• special symbols can denote outliers

Question 15

time plot

Answer 15

• for some quantitative data, we are measuring 1 subject at many time points (rather than measuring our variable across many subjects)
• plots each observation against the time at which it was measured
• 2 patterns: cycle (regular up & down movements over time) & trend (a long-term upward/downward movement over time)