week 3 -- Summarizing data & Comparing distributions

Question 1

descriptive vs inferential statistics

Answer 1

d = what we can do to DESCRIBE the population
i = what we can do to MAKE A GENERALIZED STATEMENT about the entire population based on the observed sample

Question 2

shape (descriptive)

Answer 2

symmetry?
modes (peaks)?
skew?
extreme values?

Question 3

center (descriptive)

Answer 3

MODE

MEDIAN (splits dataset down the middle – robust for extreme values)

MEAN “balances” the data (i.e., takes into account frequency), can be misleading with datasets with extreme values

Question 4

spread (descriptive)

Answer 4

RANGE (max-min)

INTERQUARTILE range (middle half of data

Median separates halves of the data

Question 5

5-number summary

Answer 5

Q1-Q3 = middle half of data
max = unusual data point? or just highest point in data?

Question 6

outlier vs extreme value

Answer 6

“outlier” is a DEFINED term (in terms of data depiction), “extreme value” is a general term

Question 7

If you draw a card at random from a well shuffled
deck, is getting an ace independent of the suit?
Explain.

Answer 7

Yes. There is the same number of aces in each suit, so no matter which suit you draw, the
probability of getting an ace does not change.

Question 8

When are descriptive stats the same as inferential?

Answer 8

When population = sample (known as a census)

Question 9

What does a bimodal pattern reflect?

Answer 9

e.g., two separate populations being lumped together – recheck trials/participants (is there anything that can explain the data?)

Question 10

Draw a boxplot

Answer 10

1) Draw small lines at the median, IQ1 and IQ3 – make a box.
2) “Fence in the data” at 1.5xIQR above and below the IQs (just for reference, not part of boxplot)
3) draw “whisker” to the most extreme values found within the fences
4) add outliers outside the fences

Question 11

What do boxplots tell us?

Answer 11

They help us compare the distribution of groups or categories we wish to compare

small IQR shows consistent performance

asymmetrical whiskers or box shows skew

outliers always derserve our attention! examine them in context of the data – is it an error or just an extreme value?

Question 12

What to compare between boxplots

Answer 12

shapes (symmetric or skewed)
medians (which is higher? any pattern?)
IQRs (which group is more spread out? any pattern to IQR change?
outliers)