CSU Stat 301 Final

confidence interval

a range of values with the purpose of capturing the value of an unknown population parameter

reasons for CIs

-point estimate does NOT equal parameter value

-to quantify uncertainty in estimating parameter

-to find plausible values for parameter

unknown pop parameter

a 95% CI means 95% of intervals created will contain/capture the...

greater, bigger

wider CI means _________ uncertainty & a ________ range of possible values for the unknown population parameter

narrower

big sample size makes the CI...

confidence level

the rate a CI successfully captures an unknown population parameter under repeated sampling

wider

a large confidence level and/or a large sample standard deviation makes the CI...

margin of error

maximum amount of random error a point estimate should have

- critical value x standard error(of point estimate)

standard error

the standard deviation of a collection of sample means(sampling distribution)

-σ/√n

hypothesis test(significance test)

test the evidence provided by the collected data that the value of the parameter supports some claim

null hypothesis (Ho)

A statement of no difference or no relationship between variables

statistical significance

when a hypothesis test is performed and Ho is rejected

alternative hypothesis (Ha)

Hypothesis in which there are nonzero effects and there are differences between treatments

p value

probability of calculating test stat from a random set of data that's at least as large as the one calculated if null hypothesis were true

-range from 0-1

-can not be negative

t-test statistic

alternate hypothesis test that measures point estimate distance from standard errors

-can be negative

reject Ho

p value < 0.05

what is means to reject Ho(µ)

the difference between the population means a so large that it is not due to chance

FTR Ho

p value > 0.05

reject null

| t | > 2

FTR null

| t | < 2

statistic

mean of the differences in our sample

parameter

mean of the differences in the population

type 1 error

occurs when Ho is rejected, but Ho is true

type 2 error

occurs when a researcher fails to reject the Ho, but Ho is false

power

probability one does NOT commit a type 2 error, when Ho is false

-you reject Ho when Ho is false

-want this to be as high as possible

effect size & sample size

what determines power

-direct relationships(when one increases, the other increases)

paired data

Study designs that involve making two observations on the same individual, or one observation on each of two similar individuals

-Ho = µ change (equation)

unpaired data

observations are independent of each other(done on separate groups)

-Ho = µ-µ (equation)

decrease

if p-value is increased then t will....

(inverse relationship, the opposite is true too)

sampling distribution

gives values a stat takes on & how often these values are taken on under repeated sampling

distribution

gives the values a variable takes on

less

increase in z-score means outcome is ____ likely to occur (& vice versa)

normal

as n(sample size) increases sampling distribution becomes more...

z-score

number of standard deviations from average

theoretical regression equation

yᵢ = ßₒ + ß₁xᵢ + ԑᵢ

response variable for observation "i"

yᵢ

population intercept

ßₒ

population slope

ß₁

-often test if this equals zero

predictor variable

xᵢ

normally distributed random variation

ԑᵢ

estimated regression equation

ŷᵢ = bₒ + b₁xᵢ

predicted value of response variable

ŷᵢ

estimated intercept

bₒ

estimated slope

b₁

R squared(R²)

proportion of variation in response variable as explained/attributed by predictor variable

slope in multiple regression

predicted change in response variable for one unit increase in predictor variable while holding all other predictor variables constant

statistic inference

process of taking information about the sample and applying it to the population

sampling bias

when the sample taken differs systematically from population of interest

self-selection bias

when individual decides if they are included in a study and their choice relates to whats being measured

non-response bias

when respondents are less likely to participate in a survey due to a reason related to the variable being studied

ANOVA

an extension of 2-sample t-test, that compares average "between group" variance to average "within group" variance

residual(error)

difference between actual observed y value and the predicted y value at observed x value