Lecture 3

Mean

Mean= sum of the observations/ number of observations

Median

The level below (or above) half of the observations fall (50 percentile).

1. Arrange your numbers in numerical order

2. Count how many numbers you have

3. If you have an odd number of values, its the # in the middle

4. If you have an even number, its the average of the two middle numbers

Most

The number that appears the most

Example of Mean, Median, Mode

1, 1, 2, 3, 4, 5, 24

Sum= 40

Mean is 6.66

Median is 3

Mode is 1

Negatively Skewed

Normal (No Skew)

Positively Skewed

Medians versus Mean?

Median is better than mean for skewed data. Outliers can greatly skew the mean.

In what direction is the skew?

The tail

Probability (Pr)

The numerical expression of the likelihood of a measurable event happening. Expressed in fractions, decimal fractions, or percent

Simple Probability

Looks at the likelihood of one event occurring (or not)

EX: What is the probability of throwing a 3 with one roll of one die?

1/6 or 16.6%

Conditional Probability

Looks at two events occurring in relation to each one. Assesses the probability of a second event occurring based on the probability of the first event occurring.

EX: 120 people attended a banquet, 100 attendees ate turkey, of those 100 80 people got sick

What is the probability of getting sick, given that a person ate turkey?

80/100=80%

Target Population

The collection of individuals, items, or measurements on which we want to study and develop inferences

Measurement Error

The initial goal is to make a study that is accurate, but all measurements are susceptible to error. The 2 types of error are: Random (imprecision) and Systematic (bias)

Standard Error of Measurement (random error)

Standard Error of Measurement is the variability of a sample measure… based on when, how and by whom the samples are obtained

Courses of variations:

Natural variations (ex. morning vs night)

Imprecise instruments

Individual difference (ex. subjective pain rating)

Sampling Error

A bias in which a sample is collected in such a way that some members of the intended population have a lower or higher sampling probability than others

EX:

Self-selection bias

Survivorship bias

healthy worker bias

Random Sampling

Attempt to replicate the characteristics of the Target Population within the drawn sample. This reduced systemic bias.

Confidence Intervals (CI)

A confidence level is a measure of the degree of reliability of a confidence interval of a variable under study. The most frequently used confidence levels are 90%, 95%, and 99%.

What P value gets papers published?

0.05, 5%

What is the lowest fraction of error P value?

0.01, 1%