COURSEWIDE

Predicted y-value

Predicted y-value

hatted y

y-intercept

b sub 0

Slope

b sub 1

Correlation coefficient

r²

Least squares regression line

LSRL

Individual data value

x sub i

Sample mean

lined x

Population mean

mu

Sum

sigma

Sample variance

s²

Population variance

Sample standard deviation

Population standard deviation

The lowest number in a set of data

min

The 25 percentile

Q1 (the first quartile)

The 50 percentile

med (median)

The 75 percentile

Q3 (the third quartile)

The highest number in a set of data

max

Measures how many standard deviations a value is from the mean

z

Mean of a sampling distribution of sample proportions

mu sub hatted p

Standard deviation of a sampling distribution of sample proportions

Mean of a sampling distribution of sample means

mu sub lined x

Standard deviation of a sampling distribution of sample means

Significance level ALSO prob of type 1 error

bar graph

categorical data

pie charts

categorical data usually for displaying parts of a whole

histograms

discrete numerical data

bar graphs what to look for

frequently & infequently occuring categories

pie charts what to look for

categories that form large or small prportions of the data set

dot plots

used with numerical data EITHER continuous or discrete

stem and leaf plots

used with univariate numerical data and MUST have key. numerical data (small to medium sets)

histograms what to look for

center & spread if data, type of distribution and unusual vlaues

Histograms

needs variety of data

cumulative relative frequency

used to answer questions about percentiles

cumulative relative frequency

contains quartiles every 25%

IQR (interquartile range)

Q3-Q1

CUSS =

Center, unusual features, shape, spread

number of pages in a book

discrete

the lifetime of a lightbulb

continuous

The mpg of a car

continuous

the distance that someone throws a baseball

continuous

The # of questions asked during a statistics final exam

discrete

continuous data

Numerical data values that can be MEASURED

discrete data

Data that can only take certain values.

When are pie charts particularly useful?

For finding the part percent of a whole out of 100%

frequency table

A table for organizing a set of data that shows the number of times each item or number appears.

relative frequency table

Shows the percents (relative frequencies) of observations in each category or class.

roundoff error

The difference between the calculated approximation of a number and its exact mathematical value. (close to 100% but not exactly, 99.9%)

bar graph

a graph that uses vertical or horizontal bars to show comparisons among two or more items

pie chart

a chart that shows the relationship of a part to a whole (exact percentages)

marginal distribution

one of the categorical variables in a two-way table of counts is the distribution of values of that variable among all individuals described by the table

two way table

a table of counts that summarizes data on the relationship between two categorical variables for some group of individuals

dot plots

a graph where dots that represent the value of data are plotted above a number line

shape

skewed, symmetric, unimodal/bimodal

center

approximate middle part of data distribution

spread

cluster, wide spread

outlier

an extreme deviation from the mean

stem plot

A graphical display of quantitative data that involves splitting the individual values into two components. The stem is the first part of the number and the second is added as the second number, etc. Remember to add a key

back-to-back stem plot

Data for one stem-and-leaf is on the right of the stem, the other is on the left of the stem.

histogram

A graph of vertical bars representing the frequency distribution of a set of data.

x bar

sample mean = sum of observations/n

mu (u)

population mean

resistant measure

A summary number that is not affected by outliers. The median is a resistant measure of center.

median

the midpoint of a distribution (resistant measure)

odd median

middle number

even median

the average of the two middle numbers

range

the difference between the highest and lowest scores in a distribution

interquartile range

Q3-Q1

1. arrange in increasing order + find median

2. median Q1

3. median Q3

4. Q3-Q1

Identifying Outliers

1. 1.5 x IQR

2. Q3 + 1.5(IQR)

3. Q1 - 1.5(IQR)

5 number summary

min, Q1, median, Q3, max

boxplots

graph based on five-number summary

boxplot on calculator

1. stat

2. edit #1

3. L1 = values

4. stat

5. calc

6. 1.1 vars stats -> L1, empty, click calculate + enter

7. use data: min, QI, median, Q3, max to make boxplot

8. stat

9. edit #4 -> L1 enter -> done

standard deviation

a measure of variability that describes an average distance of every score from the mean

variance

standard deviation squared

percentile

the pth percentile of a distribution is the value with p percent of the observations less than it

cumulative frequency column

add the counts in frequency column

cumulative relative frequency column

divide the cumulative frequency column by the total number of frequencies

standardized score (z-score)

the number of standard deviations and the direction from the mean that an observation falls

density curve

A mathematical model used to describe the overall pattern of the distribution of a random variable.

normal curve (normal distribution)

a symmetrical, bell-shaped curve that describes the distribution of many types of data; most scores fall near the mean (about 68 percent fall within one standard deviation of it) and fewer and fewer near the extremes.

empirical rule

68-95-99.7

response variable

a variable that measures an outcome or result of a study (y-axis)

explanatory variable

A variable that helps explain or influences changes in a response variable. (x-axis)

scatterplot

shows the relationship between two quantitative variables measured on the same individuals

scatterplot description

direction (pos/neg), form/shape, strength (correlation), outliers

positive association scatterplot

both variables in the same directions

negative association scatterplot

variable going in opposite directions

Correlation (r)

measures the direction and strength of the linear relationship between two quantitative variables

r on calculator

1. stat

2. edit

3. stat

4. calc 8

Least-Squares Regression Line

the line that makes the sum of the squared residuals as small as possible

extrapolation

Use of a regression line for prediction far outside the interval of values of the explanatory variable x used to obtain the line.

residual

the difference between an observed value of the response variable and the value predicted by the regression line

residual plot

a scatterplot of the regression residuals against the explanatory variable (should look random)

positive residual

model or predicted values underestimate the actual data value

negative residual

the predicted value is too big, an overestimate

good fit for residual plot

random, centered at 0, no clear patterns

coefficient of determination (r^2)

The fraction of the variation in the values of y that is accounted for by the least-squares regression line of y on x.

high leverage points

observations with extreme values for the independent variables

high magnitude points

outliers on the y-axis

experiment

A research method in which an investigator manipulates one or more factors to observe the effect on some behavior or mental process