Statics Quiz 1

Unit 1 + Unit 2 until correlation

Statistics

The set of methods for obtaining organizing summarizing presenting and analyzing data

Population

The totality of individuals about which we want information

Sample

A subset of the units in a population that is actually examined to gather information

Individual

A person animal place thing or other unit on which characteristics are measured

Variable

A characteristic or property of an individual

Categorical data

Data representing values that place individuals into one of several groups

Categorical ordinal data

Categorical data whose values have a meaningful logical ordering

Categorical nominal data

Categorical data whose values do not have a meaningful logical ordering

Quantitative data

Data representing numerical values for which arithmetic operations such as adding and averaging make sense

Continuous variable

A quantitative variable that can take any value within a given range

Discrete variable

A quantitative variable that can take only certain values

Data distribution

A description of what values a variable takes and how often those values occur

Frequency

The number of observations falling into a particular category or interval

Frequency distribution

A count of how many data values fall into predetermined classes or intervals

Relative frequency

The proportion of observations falling into a particular category or interval

Proportion

A decimal representation of a fraction with values between 0 and 1

Bar chart

A graph displaying categorical variable values and their frequencies

Pie chart

A graph showing the relative frequencies of the observed values of a categorical variable

Histogram

A graphical display of the count or proportion of quantitative data values falling into intervals

Symmetric distribution

A distribution whose center divides it into two approximate mirror images

Right-skewed distribution

A distribution whose right tail extends much farther than its left tail

Left-skewed distribution

A distribution whose left tail extends much farther than its right tail

Tail

The portion of a distribution that extends farther from its center

Time plot

A graph showing values of a variable measured over time

Time series data

Values of a variable measured over time

Seasonal variation

A repeating pattern or trend associated with different times or seasons

Location

The position of the center of a data distribution

Mode

The most frequently observed data value

Median

The middle value of an ordered data set

Mean

The average found by adding all data values and dividing by the number of values

Sample mean

The mean calculated from a sample and denoted by x̄

Weighted mean

A mean in which different data values are assigned different weights

Outlier

An extreme observation that can strongly affect some numerical summaries

Resistant

Describes a statistic that is not strongly affected by outliers

Variability

How spread out the data values are

Range

The maximum data value minus the minimum data value

Interquartile range (IQR)

The length of the interval containing the middle 50% of ordered observations

First quartile (Q1)

The value below which approximately 25% of the data fall

Third quartile (Q3)

The value below which approximately 75% of the data fall

Percentile

The ordered observation such that at least p% of the data values are as small or smaller

Five-number summary

The minimum Q1 median Q3 and maximum

Quantile boxplot

A boxplot with a median line a box covering the IQR and whiskers extending to the minimum and maximum

Side-by-side boxplots

Boxplots used to compare the same variable for samples from different populations

Outlier boxplot

A modified boxplot that identifies observations outside the lower and upper fences

Lower fence

The value Q1 − 1.5(IQR)

Upper fence

The value Q3 + 1.5(IQR)

Variance

A measure of variability based on squared deviations from the sample mean

Sample variance

The sum of squared deviations from the sample mean divided by n − 1

Standard deviation

The positive square root of the sample variance

Sum of deviations

The sum of all deviations from the sample mean which is always zero

Explanatory variable

A variable that helps explain or predict the outcome of a study

Response variable

A variable representing the outcome of a study

Scatterplot

A graph displaying the values of two quantitative variables measured on the same individuals

Association

The relationship between two variables

Direction

The direction in which the pattern of points in a scatterplot moves

Positive association

An association in which the pattern of points slopes upward from left to right

Negative association

An association in which the pattern of points slopes downward from left to right

Form

The general shape of the relationship between two variables

Linear relationship

A relationship that can be reasonably approximated by a straight line

Strength

How closely the points follow a particular form such as a straight line

Correlation

A numerical measure of the direction and strength of a linear relationship between two quantitative variables

Correlation coefficient r

A number measuring the direction and strength of a linear relationship between two quantitative variables

Perfect positive linear relationship

A linear relationship with r = 1

Perfect negative linear relationship

A linear relationship with r = −1

Weak linear relationship

A linear relationship with a correlation close to zero

Strong linear relationship

A linear relationship with a correlation close to −1 or 1

Lurking variable

A variable that helps explain the relationship between variables but is not included in the study

Association versus causation

The distinction between variables being related and one variable actually causing changes in another

Causation

A relationship in which a change in one variable directly produces a change in another

Properties of correlation

The correlation r lies between −1 and 1 has no units is unaffected by changes in measurement units and is strongly affected by outliers

Correlation and direction

Positive r indicates positive association and negative r indicates negative association

Correlation and strength

Values of r close to −1 or 1 indicate strong linear association while values close to zero indicate weak linear association

Correlation and units

Correlation has no units and is unchanged when the measurement units of the variables are changed

Correlation and variable roles

Correlation does not distinguish between X and Y so explanatory and response variables are not required

Correlation and linearity

Correlation measures only the strength of a linear relationship and may be unhelpful for nonlinear relationships

Correlation and outliers

Correlation is strongly affected by outliers

Association does not imply causation

A correlation between two variables does not establish that one variable causes the othe