Stats 261 Exam 1

Examples of Variability

Examples of Variability

gas prices, height, weight

3 main reasons to study statistics

to be informed, make good decisions, evaluating decisions that effect me

population

the set of all individuals of interest

sample

a subset of individuals selected from the population (representative group of a population)

parameter

numerical characteristic of a population, fixed quantity

statistic

numerical characteristic of a sample, variable quantity

statistical questions

a question that is answered by collecting data that varies

what is needed to determine if a question is statistical

the population, the variable that is being measured, and the variation that occurs in the variable

variable

any characteristic observed in a study

descriptive statistics

methods of organizing and summarizing information

what is the purpose of descriptive statistics

to reduce the data to simple summaries without losing too much information

what is descriptive statistics used with?

samples or with a population data set

inferential statistics

methods for drawing conclusions about a population

what is inferential statistics based on?

samples

what is inferential statistics used with?

sample data

key words for descriptive stats

summarize, record, reflect, reduce

key words for inferential stats

concluding, predicting, estimating

categorical variable

non numerical groups or categories present

quantitative variable

numerical variable

discrete

possible values form a set of separate numbers

example of discrete

number of books, shoe size, number of apples

continuous

its possible values form a continuum of values over the real number line

example of continuous

distance, height, weight

we can …. discrete variables

count

we can … continuous variables

measure

frequency distribution

a listing of distinct categories and their counts

relative frequency distribution

a listing of distinct values and their relative frequencies

what is the use of a relative frequency distribution

compare samples especially when they samples are unequal

Pareto diagram

a type of bar graph where the categories are order by their counts from the tallest bar to the shortest bar in descending order

pie chart

circle divided into wedge shape pieces proportional to their relative frequencies

what are pie charts best used for

data sets with less than 8 categories

what are graphical displays for categorical data sets

pie chart, Pareto diagram, and bar charts

mean

sum of observations divided by the number of observations

median

middle

mode

any value that occurs with the greatest frequency

what is sensitive to extreme values

mean

what isn’t sensitive to extreme values

percentiles

indicate the point below which percentage of observations occur

quartiles

divides the data into quarters

1st quartile

median of the lower half of data

2nd quartile

the median of the data

3rd quartile

median of the upper half of data

standard deviation

the square root of the variance

interquartile range (IQR)

the difference between Q3 and Q1

what does the IQR tell us

how spread out the middle 50% of data is

Range

max-min

why isn’t range used more

it only takes into account the largest and the smallest observations, might not be indicative of the trend due to being extreme

examples of quantitative graphs

dot plots, histograms, boxplots, density plots, comparative bar charts, and time plots

dot plots

display individual values of a data set

histograms

bar graph, but the categories touch

density plot

a smoothed histogram that is useful for determining the shape of the data

boxplot

a graph of the five number summary

what is the five number summary?

minimum, Q1, median, Q3, and max

time plots

used to show changes over time

what are the components of SOCS

shape, outliers, center, and spread

when do we use SOCS?

when we are asked to describe the distribution of a quantitative variable

Modality

number of peaks

unimodal

1 peak

bimodal

2 peaks

multimodal

more than 2 peaks

left skewed

negatively skewed, left tail extends longer than the right tail

right skewed

positively skewed, right tail extends longer than the left tail

outliers

unusual values, separate from the rest of the data

when do we use the median to describe data?

when the data is skewed

when do we use the mean to describe data?

when the data isn’t skewed

center

symmetric, reports the mean

spread

reports the standard deviation

do symmetric distributions have outliers?

No

do skewed distributions have outliers?

they can

bivariate data

data that has two variables

response variable

measured to make comparisons between two groups

explanatory variable

explains the value of the response variable

contingency variable

a frequency distribution for bivariate data

cell

each row+column combination

How to determine if there is an association between two categorical variables

compare row % of observations within each category of the group variable for each category. See if the response changes across the groups and if it changes there is an association

what is the range of difference for determining if there is an association between two categorical variables?

5-10% means there is an association

comparative bar chart

a bar chart that compares the conditional proportions of the response within each category of the grouping variable

positive association

as values of one variable increase, so do the values of the other

negative association

as the values of one variable increase, the values of the other decrease

no association

no relationship, neutral

correlation

measure of the strength and direction of the linear relationship between two models

magnitude

indicates the strength of the linear relationship

direction

the sign of the correlation coefficient, indicates the direction of the association

how do I know if the relationship is strong or weak from a numerical standpoint

closer to 1 or -1 means it has a stronger association

what to include in a description of the correlation coefficient

1. type of relationship (linear)

2. strength of association (weak, moderate, strong)

3. direction of association (positive or negative)

4. context (between the variables x and y)

probability

chance of an event occurring

subjective probability

you decide the likelihood EX: what are the chances I do my homework?

theoretical probability

based on a formula EX: when flipping a coin you have a 50% of either heads or tails

experimental probability

based on the results of a random experiment EX: flipping a coin 10 times and using the amount of times you obtain heads to estimate the prob. of getting heads

sample space

collection of all events and outcomes in an experiment

observation

the observed outcomes of a random experiment

event

a subset of the sample, a collection of outcomes

complement

the subset of all outcomes with the sample space that are NOT in event A, “opposite”

intersection

the event containing all the elements that are common to both A and B, “overlap”

Union

The event containing all of the elements that belong to only A, only B, or both, “combination”

mutually exclusive

events that have no outcomes in common, cannot happen at the same time

Formula for complements

P(A^c)=1-P(A)

Formula for Unions

P(A and B)= P(A)+P(B)-P(B)-P(A and B)

Marginal

an individual event probability