Stats Test 1

Statistical investigation process

1. Ask a statistical question

2. Collect data

3. Analyze data

4. Draw conclusions

Anecdotal evidence

Personal observations, hearsay, or unusual examples to draw conclusions

Population

the set of individuals or things we wish to know about

Parameter

a numeric characteristic of the population

Data

Facts or piece of information that can be used to gain knowledge or make decisions

Variable

A characteristic that takes on different values across individuals or objects

Census

Data are collected from EVERY member of the population

Quantitative

Numerical variable

Qualitative

Categorical variable

Distribution

Pattern of the outcomes

Exploratory data analysis

the process of using summaries of the data to identify patterns, trends, and unexpected outcomes. AKA “data summary”

Describing center

The most common summaries are the mean and median

Describing ‘spread’ (variability)

Variance and standard deviation

Percentiles

split the data by percentages. The median is the 50th percentile

Quantiles

Percentiles in decimal values

Quartiles

Specific percentiles

Interquartile range (IQR)

Q3-Q1

Observational study

Observe subjects and measure variables of interest but do not intervene. Cannot show change in one variable causes a change in the other.

Association

does NOT = causation

Confounding variable

Associated with both the explanatory and response variables and can explain the relationship between them

Positive relationship

As one variable increases, so does the other

Negative relationship

As one variable increases, the other decreases

Strong relationship

Given a value of one variable, it is possible to make a good estimate of the value of the other

Weak relationship

Given a value of one variable, we still can’t say much about the value of the other

Correlation

A number that describes the strength and direction of a linear relationship

Correlation coefficent

Denoted “r”. -1<r<1.

Linear regression

Line that summarizes the bivariate data. This line can estimate values of the dependent variable.

Residual

Indicates the vertical distance between observed (actual) data point and the value predicted by a statistical model.

Population mean symbol

u

Population proportion symbol

μ

Population standard deviation

σ

Population variance symbol

σ²

Sample proportion symbol

p hat

sample standard deviation symbol

S

Sample variance

S²

Sample mean symbol

X bar