stat midterm 2

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s^2 pooled

(df1* s^2 sub1)/df total +(df2*s^2 sub 2)/df total

test statistic formula

(sample statistic-population parameter)/standard error of sample statistic; xbar-mew/Ssubxbar

variable criteria for rejecting null in independent sample

(xbar1-xbar2)cv= tcv(s subxbar1-sbar2)

steps recommended for evaluating the null hypothesis

1. decide level of significance 2. decide if its directional or nondirectional 3. outline the critical value of the test statistic and sample statistic

steps to interpreting results of sample statistic

1. decide whether or not statistically significant 2. if so, calculate the effect size, consider practical significance 3. state results in plain english

steps to eyeball estimate the confidence interval of a sample histogram

1. eyeball estimate the mean with balance point 2. eyeball estimate the standard deviation at points of inflection 3. eyeball estimate the standard error by dividing that by estimated sample size 4. for 95% confidence interval double the standard error in each direction to find the confidence interval

how is it different evaluating a test statistic in one tailed v two tailed tests?

1. hypothesis is one directional only 2. Level of significance all on one side 3. only one critical value and rejection region

4 steps of hypothesis testing

1. state the null and alternative hypothesis 2. establish criteria for rejecting the null 3. collect a sample of the sample statistic and compute the sample and test statistics 4. evaluate whether we should reject or fail to reject the null

z cv if apha is .05 and test is directioal

1.645

z cv if alpha is .05 and test is nondirectional

1.96

for sample size greater than _____ t subcv is about ____

10; 2

"rarely" in psychological statistics

5% of the the time

population proportion symbol and meaning

Pi-- same as population mean, mew

formula tobs independent sample

[xbar sub 1- xbar sub 2]/(s sub x1bar-x2bar); (sample 1 mean- sample 2 mean) divided by standard error of the difference of means

how far does the confidence interval extend for 95% confidence?

about two standard errors each direction from x bar

distribution of the variable shows...

all possible values of x if the null hypothesis is true

distribution of the test statistic shows

all possible values of z if the null hypothesis is true

probability of making type I error

alpha

level of significance

alpha or the setting of probability

95% statistical significance

alpha: .05

treatment variable

another name for independent variable which defines group memebership

effect of sample size on t obs

as sample size increases, t obs increases

why do we pool variances?

assuming the variances are equal under the null hypothesis the pooled variance of two samples is a more accurate point estimator of the population parameter

why might data in a one tailed test reject the null when it doesn't in a two tailed test? What about vice-versa?

bc the rejection region all lies on one side such the region there is bigger. but if

when do we set the critical value of the statistic?

before the experiment (research design)

probability of making type II error

beta

rejection region limits

beyond critical value(s) of the sample statistic

alternative name for type II error

bliindness error

effect size index

d= (xbar- mew)/standard deviation

dependent samples variable cv formula

dbar cv= tcrit*s sub d bar

practical significance

degree to which our result is actually important; how large the difference is in the real world importance

statistical significance

degree to which our result is not likely to be due simply to chance

descriptive statistics

describing statistical information in terms of a distribution

df pooled variance

dfpoooed is df1+df2

repeated measures design

experiment in which the same participant is measured multiple times

true experiment

experimenter has total control over the treatment variable and randomly assigns membership

if our hypothesis test falls within the null hypothesis we

fail to reject the null hypothesis and assume no change was made

standard error of the difference of two means is ___ than the ____ by a factor of ____

greater; standard error of the mean; sq rt 2

examples of what is not a true experiment

group membership defined by natural or uncontrolled occurrence such as gender, age, marital status, or height

alternative name for type I error

gullibility error

null hypothesis in a directional, single variable test

h0: x>a OR x<a

making the level of significance smaller makes the

harder to reject the null hypothesis

measure of effect size quantify

how far apart two curves are

how to tell between questions asking about confidence interval or hypothesis test?

hypothesis tests are in the form of yes/no while confidence interval might ask what could be inferred about a population when we only have sample mean

width of confidence interval is ____ to the ______ _______ the critical values

identical; width between

how do you use confidence interval for hypothesis testing?

if the mean of the null hypothesis lies in the confidence interval of the observed hypothesis

robust

insensitive to violations of the assumptions meaning that in

what is the standard error of the distribution of means?

it's the standard deviation of a single x bar divided by square root n

standard effect size; formula

magnitude of a result's distance from null hypothesis given in standard deviations; d= lxbar-mewl/sigma

raw effect size

magnitude of a result's distance from null hypothesis in the scale of original experiment

effect size

magnitude of our statistical result

making the level of significance smaller effects the rejection region how?

makes it further from the mean and thus the criterion for rejection more stringent

null hypothesis in independent sample test (two ways)

mu1=mu2 OR mu1-mu2=0

for the same sample size and same critical value, the graph of the confidence interval is ____ for known sigma vs an unknown sigma

narrower

degrees of freedom in dependent samples

number of difference scores-1

degrees of freedom

number of observations, minus one

raw effect size formula

numerator of the null hypothesis in question

difference between the critical value of sample statistic and that of the test statistic?

only the scaling such that the test statistic is standarized

sample proportion (symbol and statistical equivalent)

p-- same as sample mean, x bar

the _____ variance is always _______ variance x sub 1 and variance xsub 2

pooled; between

rejection region

region of z axis beyond critical value

proportional standard deviation (symbol and equation) for yes and no answers

s sub p= square root(p*(1-p)/n-1) where p= "proportion of no's (or yes')"

standard error of the differences of means symbo

s sub xbar1-xbar2

equation sample standard error

s/square root n

formula pooled variance with different sample sizes

s^2 (sub pooled)_= [(s^2 sub 1)(dfsub1)+(s^2 sub 2) (dfsub2)]/[f total; pooled variance is variance1 times degrees of freedom1 plus variance 2 times degrees of freedom 2 all divided by the degrees of freedom1 plus degrees of freedom

formula s^2xbar, s^2ybar in independent samples; in words

s^xbar=s^2pooled/nx, s^ybar=s^2pooled/ny; standard deviation of the mean xbar= pooled variance divided by sample size of x, variance of mean ybar= pooled variance/sample size y

tcv for independent test

same as tcv for any test: define alpha, look at TOTAL degrees of freedom and correct column for one tailed or two tailed test

effect of sample size on effect size

sample size doesn't effect effect size

inferential statistics

seeks to draw conclusions about the world from statistics

distribution of the sample statistic

shows all possible values of the sample mean x bar if the null hypothesis is true

equation population standard error

sigma/square root n

recommended steps to "state null and alt hypothesis"

sketch 3 distributions: that of the null hypothesis, the distribution of x bar, distribution of the test statistic

___ standard deviation makes it more likely to reject the null

smaller

larger the sample size and smaller the s sub D, the _____ the required ____ ______ Dbar obs and ____

smaller; distance between; zero

the standard error is ___ than the standard deviation by a factor of ____

smaller; sq rt n

formula for standard error of the difference of means

sq root (ssubxbar1+ssubxbar2) OR s sub x1bar-x2bar=square rt (s^2pooled/n1)+sq root (s^2pooled/n2); standard error of the difference of means is: variance of sample1 plus variance of sample 2 all square rooted

formula standard deviation of the difference of means

sq rt (s^2pooled/n1 + s^2pooled/n2)

standard error of the difference of means conceptually

standard deviation of the distribution that would occur from creating a sample of means of the difference between xbar1 and xbar2 with infinite samples

why do we use standard error to calculate confidence interval as opposed to standard deviation? How does it change the equation? Why?

standard error is narrower than standard deviation because the distribution of means is narrower than that of a single sample according the central limit thrm; we use this narrower range for the confidence interval because we want to find the population mean not the population range of values and we believe by the central limit thrm it will fall between about 2 standard errors of any sample mean we pull

denominator of independent sample

standard error of the difference between means (s sub xbar1-sbar2)

equation for xbar sub obsv

summationX/n

how does t observed relate to t cv?

t observed is the value we calculate which shows up either in the rejection region (beyond the t cv) or not showing us whether or not too reject the null hypothesis

critical value of the statstic on standard scale (symbol and definition)

t sub cv; beginning of the rejection region such that if our observed value lies beyond this we reject the null hypothesis

to pool is to

take weighted average of variances

directional test

testing an alternative hypothesis which is either greater than or less than the null hypothesis, thus having direction of change

nondirectional test

testing an alternative hypothesis without a claim of any particular direction

which sample statistic do you use in a test statistic?q

the best point estimate of the population parameter of interested

x1 and x2 are strongly correlated in dependent samples test; effect of this

the differences are about equal throughout; this makes the s sub d and s sub dbar large such that t obs will be large

null hypothesis

the hypothesis that nothing has changed

alternative hypothesis

the hypothesis that things have changed

sigma subx1bar-x2bar in relation to sigma sub xbar

the independent sample standard error of the means is larger by a factor of sq rt two than the standard error of population means

which population parameter do we use in the test statistic?

the null hypothesis parameter

xbar1-xbar2 cv (concept)

the point(s) beyond which the rejecction region lies in a pooled independent sample: tcv*(s sub xbar1-xbar2)

statistical power

the probability of correctly rejecting the null hypothesis; 1-beta (either we are correct or we make a type II error)

alpha

the probability of making a type I error

beta

the probability of making a type II error

level of significance

the probability we accept in order to reject the null hypothesis

difference score

the score for the difference between two matched samples

which sample standard deviation do you use in a test statistic?

the sd of the sample statistic we used in the numerator

standard error of the mean of differences conceptually

the standard deviation of the samples from two populations making dbars again and again infinitely

if d=0

the two curves overlap (observed and null hypothesis)

t observed conceptually

the value we observe for test statistic of the sample representing the population data as expressed on the standard scale

what distributions can (or cannot) have rejection regions?

the variable of sampling statistic or the variable of test statistic (not the dist of the variable under the null hypothesis)

what is the purpose of a confidence interval

to try to find mew within a range of probability

which error type is worse to make? why?

type one error because it makes claims of change that don't occur; type two error usually does not result in a significant paper just in subsequent experimentation

dependent variable

variable of primary interest in a study

independent variable

variable that defines group membership

where is mew along the confidence interval?

we don't know, but we hope it falls on the interval

if our hypothesis test falls within the alternative hypothesis

we reject the null hypothesis and assume change occurs because of our variable

when do we use test statistic z vs. test statistic t?

we use test statistic z when sigma is known we use test statistic t when sigma is unknown and thus we calculate s

ways to be correct in hypothesis testing

when we fail to reject the null hypothesis and it actually makes no difference in nature; if we reject the null hypothesis and change actually occurs in nature

type 2 error

when we fail to reject the null hypothesis but it was actually false (change made in nature); concluding no effect exists when it actually does

type 1 error

when we reject the null hypothesis but it actually is true (makes no change); concluding that an effect exists when it actually doesn't

for the same (small) sample size and same alpha, the graph of the confidence interval is ____ for unknown sigma vs a known sigma

wider

the t distribution is ___ than the z distribution

wider and shorter

how do we reject the null hypothesis?

with the critical values or confidence interval

what's the center-most point of the confidence interval?

x bar

observed value of the statistic (symbol and definition)

x bar sub obsv; a computed statistic of our sample (mean?) distribution

calculation confidence interval

xbar+/- tcrit*s sub x bar; point estimate of mew plus or minus the standard critical value multiplied by the standard error of the point estimate

standardized effect size independent samples

xbar1- xbar2/ spooled; mean1-mean2 all divided by the pooled standard deviation

standard effect size of independent samples

xbar1-xbar2/spooled

equation for critical value of the sample statistic

xbarsubcv= mew+ z subcv* sigma subxbar

x cv calculation

xcv= tcv(s sub xbar) -/+ mu (if repeated or independent mu is assumed zero)

what is the difference between looking up a critical value in z distribution and t distribution? When do you use each?

you use the z you look up the z value and when you use t you look up the degrees of freedom; you use z when sigma (population standard deviation) is known and t when only have sample standard deviation

what is the difference numerically between zcv and tcv?

zcv is always the same wheras tcv is dependent upon df


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