STATS 7 - Quiz 2 (LO3, LO4, LO5, LO6)

Categorical variable

The value of the variable consists of groups and categories that don’t have any logical ordering.

Quantitative variable

The raw data consists of numerical measurements on each individual/units or they consist of counts

Easiest way to identify categorical or quantitative variable?

Categorical variables are statements and quantitative variables are numbers

Bar graphs

Each characteristic, or level, is represented by a bar. The height of a bar represents either the count of individuals with that characteristic, the frequency, or the percent of individuals with that characteristic, the relative frequency.

Pie charts

A pie chart can only represent how one categorical variable breaks down into its components. Each characteristic is represented by a slice, and the size of a slice represents what percent of the whole is made up by that characteristic.

Histograms

A summary graph for a single quantitative variable. Useful to understand the pattern of variability in the data, especially for large data sets

Line graphs (time series plot)

Use them when there is a meaningful sequence, like time. The line connecting the points helps emphasize any change over time

Symmetric distribution

Left skew

Right skew

Outliers

An important kind of deviation in the distribution of the data is an outlier. Outliers are observations that lie outside the overall pattern of a distribution. Always look for outliers and try to explain them.

Graphing time series

Data collected over time are displayed in a time plot, with time on the horizontal axis and the variable of interest on the vertical axis

We look for a possible trend and possible cyclical variations

Long-term trend

Variables change steadily over time

Seasonal components

Trend to be high in certain months or seasons and low in other years

Irregular Cycles and Random Fluctuations

Irregular cycles may be explained by social, environmental, political, or other factors

Unexplainable random fluctuations are part of the natural variabiltiy present in all measurements

Mean (or average)

Add all values and then divide by the number of values

Median

The middle value after the numbers have been put in order

Mode

Most common value in a dataset

Comparing median and mean

The median is a measure of center that is resistant to skew and outliers. The mean is not.

Variability

Describes how spread out or close together the data values are.

Minimum

The smallest value in the data set

Maximum

The largest value in the data set

Range

The difference between the maximum and minimum

First Quartile (Q1)

The median of the values below the median in the sorted data set

Third Quartile (Q3)

The median of the values above the mean in the sorted set

Five number summary

Minimum, Q1, Median, Q3, Maximum

Boxplots

Visual representation of five number summary

IQR

Q3 - Q1

Lower Bound

Q1 - (1.5 * IQR)

Upper Bound

Q3 + 1.5 * IQR

Standard Deviation

A useful measure of how spread out the numbers in a data set are

How to find standard deviation

Find mean, find deviation of each value to mean (value - mean), square the deviations, divide sum by number of values - 1 to find variance, square root the variance to find standard deviation

Contingency Table

Represent the counts and values of one variable in the rows and represent the counts and values of another variable in the columns

Relative risk or relative odds

Involves comparing one category to another category

percentage with the trait

(number with trait / total) x 100%

Proportion with the trait

number with trait / total

Odds of having that trait

number with trait / number without trait to 1

Relative risk

Relative risk of an outcome for two categories of an explanatory variable is the ratio of the risks of the risks of each category. (So the risk of getting allergy from owning a pet vs risk of getting allergy from not owning a pet - double calculation)

Baseline risk

Risk without the treatment or behavior. Difficult to read

Increased risk

Comparing relative risk vs baseline risk to see if your chance of gaining something has changed or not

Odds ratio

Ratio of the odds, like the relative risk of odds

Simpson’s paradox

Third variable is missing due to combining of data leading to false conclusions