Stat 250 final

data

observations gathered for analysis; numerical or non-numerical

cases

subjects we obtain data about

when making comparisons, we would like to

determine association and determine causation

statistical inference

the process of using data from a sample to gain information about the population

sampling bias

occurs when the method of selecting a sample causes the sample to differ from the population in some relevant way

we try to obtain a sample that is (?) of the population

representative

simple random sampling

all groups of the population have the same chance of being chosen

is a voluntary sample a good sampling method?

no

association

values of one variable tends to be related to values of the other variable

causation

changing the value of the explanatory variable influences the value of the response variable

T/F: association automatically means causation

no; association does not imply causation

confounding variable

third variable that is associated with both the explanatory and response variable

observational study

a study in which the researcher does not actively control the value of any variable, but simply observes the values as they naturally exist

experiment

a study in which the researcher actively controls one or more of the explanatory variables; aka randomized experiment

which study can find causation

experiment

do confounding variables exist in a randomized experiement

no

three explanations for why association may be observed in sample data

1. there is a causal relationship or association

2. there is an association, but it is due to confounding variables

3. there is no association; it is random chance

how do you avoid confounding variables

use random assignment

randomized comparative experiment

randomizing cases into different groups and then comparing results to response variable

matched pairs experiment

each case gets both treaments in random order and examine individual differences

random sampling vs random assignment

each unit has same chance of being chosen vs placing units into groups by chance

random selection allows us to

make generalizations about the population

random assignment allows us to

make conclusions about causality

frequency

number of times a value is observed in a data set

relative frequency

number of times a value is observed divided by the total number of observations

the sum of all relative frequencies is

1

one categorical variable summary statistics

frequency table, proportion

one categorical variable visualization

bar or pie chart

two categorical variable summary statistics

two-way table, difference is proportions

two categorical variable visualization

segmented or side-by-side bar chart

mode

the category that occurs most frequently

segmented bar chart

the height of each bar represents the frequency of one categorical variable and the segmented colors split each bar by the other categorical variable

side by side bar chart

separate bar charts are given for each group of one of the categorical variables

visualizing one quantitative variable

dot plot or histogram

shapes

symmetric or skewed

measures of center

mean or median

right skewed

tail of distribution extends out to the right

left skewed

tail of distribution extends out to the left

resistance

we say a statistic is resistant if it is unaffected by extreme values

which measure of center is impacted by utliers

mean

which measure of center is not impacted by outliers

median

left skewed mean vs median

mean < median

right skewed mean vs median

mean > median

standard deviation

a number that measures how far away the typical observation is from the mean

a larger standard deviation means

the data values are more spread out and have more variability

T/F: standard deviation is not affected by outliers and skeweness

false

IQR

Q3-Q1

only use the standard deviation as the measure of spread when you are using the (?) as the measure of center

mean

use this measure of center and this measure of spread when skewed

median and IQR

boxplot

graphical representation of the five-number summary

left skewed box plot

median line to the right of the box; left whisker longer

right skewed box plot

median line to the left of the box; right whisker longer

standard error

the standard deviation of the sample statistics

a low standard error means

statistics vary little from sample to sample

as the sample size increases, the variability of sample statistics tends to (?) and sample statistics tend to be (?) to the true value of the population parameter

decrease; closer

does the shape of the population affect the center of each sampling distribution?

no

confidence interval

captures parameter for a specified proportion of all samples

confidence interval formula

sample statistic ± critical value*(SE)

confidence interval interpretation

we are 95% confident that an interval captures the true population parameter

95% rule

if a distribution is approximately symmetric and bell-shaped, about 95% of the data should fall within 2 standard deviations of the mean

95% rule formula

statistic ± 2(SE)

bootstrapping

technique or simulating a sampling distribution when you do not have a population from which to sample

bootstrap sample

sample with replacement from the original sample using the same sample size

bootstrap distribution shape

bell shaped and symmetric

bootstrap distribution center

centered at sample statistic value

bootstrap confidence interval

when symmetric and bell-shaped, statistic ± 2(SE)

as the confidence level increases, the width of the confidence interval…

increases

as the sample size increases, the width of the confidence interval…

decreases

statistical test

used to determine whether results from a sample are convincing enough to allow us to conclude something about the population

goal of a hypothesis test

asses evidence provided by the sample data to test a claim made about a population parameter

null hypothesis

H-naught

alternative hypothesis

H-A

null hypothesis meaning

no change; always equals zero

alternative hypothesis meaning

claim for which we seek evidence; different from zero

hypothesis tests are always written in (?) notation

population parameter

two-sided hypothesis

H0: p1 = p2

HA: p1 does not equal p2

left-sided hypothesis

H0: p1 = p2

HA: p1 < p2

right-sided hypothesis

H0: p1 = p2

HA: p1 > p2

the null hypothesis is assumed to be (?) throughout the hypothesis test

true

how do you determine the p-value by hand?

count how many points were observed that are greater than or equal to the sample and divide that number by 100

p-value

proportion of samples that would give a statistic as extreme as the observed sample result when the null hypothesis is true

two-tailed p-value

when the alternative hypothesis contains a does not equal sign, the p-value is twice the proportion of the smallest tail

p-value < a

reject null hypothesis

p-value > a

do not reject the null hypothesis

smaller p values mean the sample results are

statistically significant

formal hypothesis test has only two possible conclusions

reject or do not reject the null hypothesis

possible significance levels

0.05, 0.01, 0.1

conclusions of hypothesis tests

conclude in terms of H-A in context of the question

type I error

occurs when we reject a true null hypothesis

type II error

occurs when we do not reject a false null hypothesis

if a = 0.05, there is a (?)% chance of a type I error

5

as a sample size increases, statistics in the randomization distribution will be more closely concentrated around the..

null value

a larger sample size (?) the chance of making a type II error

decreases

two methods of statistical inference

confidence intervals and hypothesis tests

sampling distribution

shows distribution of sample statistics obtained from a population, centered at true value of population parameter

bootstrap distribution

simulates a distribution of sample statistics for the population, centered at value of original sample statistic

randomization distribution

simulates a distribution of sample statistics for a population in which the null hypothesis is true, centered at value stated in null hypothesis

(-L, -U)

does not capture 0; reject the null hypothesis

(L, U)

does not capture 0; reject the null hypothesis

(-L, U)

captures 0; do not reject the null hypothesis