Statistics

HALG2 Stats

Experiment vs observational study

Observational study:

• watch while looking for patterns but not influencing the results.

• aims to describe a group.

• no control over it.
  

Experiment

• INFLUENCING/ doing something to change responses. You have control

• The one conducting it has control over it.

• proving a cause leads to an effect

Sample survey vs. a census

Sample survey - a small group is sampled (SRS = simple random sample) to describe a population

Census - the WHOLE population provides data

Rate vs. count

We only do rates (fractions, proportions, or percents) of people

Sample pieces:

population, parameter, sample, statistic

parameter [p]

a percent to describe a poplation. It is usually unknown, so statistics measure this.

Statistic [p-hat]

number to describe a sample (proportion)

example: sample is 500 adults, statistic is 300/500, or 60%.

Mean & median

average (sum over number of pieces)

middle piece when put in order

5 number summary

• Min: smallest piece of data

• quartile 1: average of the pieces from the min to the one before the median

• Median

• quartile 1 average of the pieces from one after the median to the max

• Max: largest piece of data

example data: 1, 3, 4, 5, 6, 7, 8
Min: 1 Max: 8 Median: 5

Q1: 8/3 Q3: 7, or 21/3

Inner quartile range

[Q1 - Median - Q3]

Box and Wisker plot

• Set a nice scale

• plot the pieces from the 5-number summary on a numberline

• make a box around the IQR

Outliers

1.5(Q3-Q1) = #

then: Q1 - # & Q3 + #

Range: [Q1 - #, Q3 + #]. If outside this range, it is an outlier

deviation (s)

spread

• measured by the standard deviation

• use the mean x as the center

same unit as OG data (if measuring in meters, its in meters)

When to use standard deviation vs. 5 number summary

• mean and Standard deviation when mean and median are close together (symmetric), as they get effected by outliers

• 5 number summary is best when there are are outliers

Properties of a normal distribution

• The mean determines the center. Everything deviates from the mean.

• all pieces of data are represented under the curve (100%)

Empirical Rule

• 34%, 13.5%, 2.35%, 0.15%.

• Anything in the 2.35 and 0.15 is an outlier

• a higher z score means higher probability (0-50%, 1-68%, 2-95%, 3-99.7%)

Normal CDF and inverse

Apps

Stat

Enter

F5

Pick one