Week 2 - data wrangling

Question 1

variables

Answer 1

characteristics that differ among individuals or other sampling units.

Question 2

categorical variables

Answer 2

Categorical variables: qualitative characteristics of individuals that do not have magnitude on a numerical scale.
Nominal - no order
Ordinal - can be ordered (letter grades)

Question 3

numerical variables

Answer 3

Numerical data: quantitative measurements that have magnitude on a numerical scale.
Continuous
Discrete

Question 4

explanatory variable
response variable

Answer 4

Explanatory variable: independent variable

Response variable: dependent variable

Question 5

frequency distribution

Answer 5

the number of times each variable occurs in a sample.

Question 6

probability distribution

Answer 6

distribution of a variable in the whole population.

Question 7

normal distribution

Answer 7

bell-shaped curve.

Question 8

sample mean

Answer 8

Sample mean: the sum of all observations in a sample divided by n, the number of observations.

Question 9

standard deviation

Answer 9

Standard deviation: a common measure of the spread of a distribution. It indicates how far the different measurements typically are from the mean.
Calculated from variance
⅔ of data within 1 sd
95% within 2 sd
Can be calculated from a frequency table

Question 10

coefficient of variation

Answer 10

Coefficient of variation: the standard deviation expressed as a percentage of the mean.
Higher CV means more variability and lower means more consistency relative to the mean

Question 11

median

Answer 11

the middle measurement of a set of observations

Question 12

interquartile range

Answer 12

the difference between the third and first quartiles of data. It is the middle 50% of the data.

Question 13

box plot

Answer 13

Displays median, interquartile range, first and third quartiles, median, smallest and largest non-extreme values (not more than 1.5x IQR from box edge

Question 14

how measures of location and spread compare

Answer 14

Mean is more sensitive to extremes than median (middle)
Standard deviation is more sensitive to extremes than mean. IQR is not and is a better measurement when there are extremes

Question 15

when does data become information?

Answer 15

when processed

Question 16

descriptions of data

Answer 16

Location (central tendency)
Width (spread)

Question 17

distributions

Answer 17

If median, mean and mode values are similar, their values will be close to normal distribution
If median, mean and mode values are not similar, data will be skewed

Question 18

Why is sample standard deviation formula divided by n-1 not n?

Answer 18

Corrects bias which occurs during the estimation process (aside from this we don’t need to know all the details about why this happens). Lose a degree of freedom

Question 19

Why do we use squared deviation in order to calculate variance (Yi - Y bar)^2?

Answer 19

Gets rid of negatives
Weights larger deviations more heavily

Question 20

estimation

Answer 20

Estimation: is the process of inferring a population parameter from sample data. The value of an estimate calculated from the data is almost never the exact same as the true value (the parameter).
Use standard error formula to see what variability we should expect and if we can trust our estimates
By repeatedly sampling tables we eventually end up with the probability distribution of all the values of an estimate we might have obtained if we sampled the population this way

Question 21

standard error

Answer 21

an estimate of the standard deviation of the sampling distribution.
Predicts the sampling error of the estimate. It can indicate uncertainty and precision
In most cases we do not have the real sampling distribution so use standard error of the mean

Question 22

sampling distribution

Answer 22

Sampling distribution: theoretical distribution of an estimate.
The larger the sample size the more narrow and precise the sampling distribution

Question 23

standard error of the mean

Answer 23

Standard error of the mean: gives us understanding of the likely difference between our sample mean and the true population mean.

Question 24

standard deviation and variance

Answer 24

Variance is larger than standard deviation
Standard deviation has same units as data values whereas variance does not

Question 25

summary

Answer 25

Estimation is the process of inferring a population parameter from sample data.
All estimates have a sampling distribution, which is the probability distribution of all possible values of the estimate that might be obtained under random sampling with a given sample size.
The standard error of an estimate is the standard deviation of its sampling distribution. It measures precision. The smaller the SE, the more precise the estimate. We can approximate this estimate, fortunately, from a single sample.
As an approximation, 95% of the time the true parameter value will lie within two SE’s plus or minus from the sample estimate.
Standard errors (and standard error bars on graph) indicate uncertainty about the sample estimates (mean, sd, median etc), NOT variability in the raw data.