Statistics Chapter 2

Descriptive Statistics

Summarizing and visualizing variables (also known as exploratory data)

Frequency Table

shows the number of cases that are in each category

Proportion

Proportion = number in category/total sample size(Sample: p^{^} (“p-hat”) & Population: p)

Relative Frequency Table

shows the proportion of cases that fall in each category

Barplot

the height of the bar corresponds to the number of cases falling

Pie Chart

the relative are of each slice of the pie corresponds to the proportion in each category (less preferable)

Difference in Proportions

difference in proportions for one categorical variable calculated for different values of the other categorical variable

Dotplot

each case is represented by a dot and dots are stacked

Histogram

the height of each bar corresponds to the number of cases within that range of variable (most important graph for quantitative data)

Mean

average of the data value. Mean = sum of all data values/number of data values (Sample: x^- & Population: u)

Median

m, is the middle value when the data are ordered. If there are even # of values, the median is the average of both values

Resistant

a statistic that is relatively unaffected by extreme values

Outlier

an observed value that is notably distinct from the other values in a dataset (smaller than: Q1-1.5(Q3-Q1) or Larger than: Q1+1.5(Q3-Q1)

Standard Deviation

a quantitative variable measures the spread of the data (Use Statkey) Sample: s & Population = o (“sigma”)

95% Rule

95% of the data will be between u-2(o) and u+2(o)

Z-score

the number of standard deviations as a value falls from the mean (Data value: Z=x-x^-/s & Population:z=x-u/o

Percentile

the percentage of all the data that are less than or equal to that value

Quartiles

are percentiles that divide the data set into quarters

Five Number Summary

Min_{(0th percentile)} Q1_{(25th percentile)} m_{(50th percentile)} Q3_{(75th percentile)} Max_{(100th percentile)}

Range

Max - Min

Interquartile Range (IQR)

Q3-Q1

Difference in Means

when comparing a quantitative variable across two categories compute the difference in means

Positive Association

value of one variable tend to be higher when values of other variables are higher

Negative Association

values of one variable tend to be lower when values of the other variable tend to be higher

Not Associated

if knowing the value of one variable does not give you any information about the values of the other variable

Scatterplot

the graph of the relationship between two quantitative variable

Correlation

a measure of strength and direction of linear association between two quantitative variables (Sample: r & Population: P (“rho”)

Equation of the Line (Variables)

y^{^}_{(Predicted response) = a}^(intercept)+ b^(slope)x_{(explanatory)}

Observed Response

y, is the response value observed for a particular data point

Precited Response Value

y^{^}, is the response value that would be predicted

Residual

each data point is observed - predicted (y-y^{^})

Least Square Lines

the line which minimizes the sum of squared residuals

Slope

Increase in predicted y for every unit increase in x

Intercept

predicted y value when x=0