Terms  Definitions 

xbar+1, +2, +3 numbers 
50%tile34.13%13.59%2.15%.14%

p>.05 
retain (fail to reject) null

P value represents... 
tail area probability

ANOVA 
stat. use for multiple IV's

zscore formula 
z= (xxbar)/ standard dev.

NonNormal(Bimodal Curve) 
mshaped. has two modes.

z = xMu/sigma (for populat)>z=xxbar/ strd dev (for sample). This is known as a ____ ______ 
transformation scaling

If cards are drawn without replacement, the probability that player 1 gets a 1 is.... 
1/3

type 1 error 
increases as alpha increases=rejecting the ho when it is true=stating IV caused the result when it was really due to chance

range 
the simplist measure. the difference between the highest and lowest scores in the distribution

cumf 
the cumulative frequency. the number of scores at or below any given score

How do you solve for z? 
(nullalternative)/Strd Error

Continuous random variables will have what kind of distribution? 
Normal distribution

For multiple choice probs where 4 choices are present, what is the probability that a student makes all 5 problems by sheer guessing? 
n=5p=1/4(p)^(n)(1/4)^(5)

Which distribution is used to determine the p value? 
sampling distribution

Deviation 
the difference between a given score and the mean of the distribution D=x  xbar

NonNormal(Ogive Curve) 
sshaped curve. either all high scores or all low scores.

f 
the frequency with which each score occurs in the data

Normal(Leptokurtic Curve) 
small standard dev. (scores all bunched up around mean)

percentiles can also be seen as...((13.59%)) 
probabilities ((P=.1359))

type 2 error 
increases as alpha gets smaller=failing to reject t he Ho when it is really false=stating the result was due to chance when was due to IV

mean 
mathematical average of a group of scores, the sum of the scores divided by the number of scores(most vulnerable to extreme scores)

____ error is controlled and minimized by setting the __ level in hypoth testing. 
Type 1, alpha

how large does sample size need to get for the central limit theorem to apply? 
30

CLT maintains that... 
all sampling distributions of any size or kind will be approximately normal regardless of the original

cumprop 
the proportion of scores at or below any given score ( take the cumf and divide by the total number of scores)

standard deviation 
the avergae deviation of all scores from the mean

Variance 
the square of a scores deviation from the mean d2=variance.

%ile 
percentage of scores at or below any given score

alpha level 
the probability of an event occuring by chance at which one is willing to reject the Ho

What type error if:the null is true but you reject it? 
type I

Something that is statistically significant... 
is not necessarily scientifically significant. Stats just lets us make a best educated guess.occurs whenever p is less than alpha and you reject the null.

What type error if:the null is false but you retain it? 
type II

Ho is a .... 
statistical decision. It's the true state of nature and has not been proven.

How do you calc the binomial p=8 when n=8 and p=1/2 
(1/2)^8

calculating standard dev. 
1. find mean of distributon2. create freq. dist. chart x(score) f(freq.) d(deviation, the scoremean) d2(variance, deviation squared) fd2(variance * freq)1 add up all the numbers in fd22 divide dum of fd2 by N3 take square root of result

Expressing pvalue 
p value = p (observed data or more extreme given the null) Alternativelypval = p(observed or more extreme  Ho)

type II error 
retain the null when the null is false=Beta

Hypothesis testing is also known as .... 
null hypothesis significance test

Type I error 
reject the null when the null is trueType I is what we try to minimize=alpha

Does a sampling distribution have anything to do with actual data? 
not reallly. The sampling distribution is a hypothetical distribution

If the original x was normally distributed, what kind of distribution will be obtained? 
Standard (Unit) normal distribution

Frequentist methods 
are the standard. Ho and H1 are not on equal footing, bias is in favor of null. Decision is based upon p value.

Logic of inferential statistics 
to decide if the difference between the experimental group mean and the control group mean was caused by the IV or just chance

definition of standard error 
standard error = strd dev of the sampling distribution

steps in taking a binomial distribution to a standard normal distribution (with z scores) 
1. W/ binomial distribution, get tailarea variables2.W/ tail area probability (p) scale to a standardized z score3. Z scores are used in a unimodal, normal distribution

above = below = 
will have a z that is positivewill have a z that is negative

The p value is the ... 
probability of obtaining a sample mean equal to the observed sample mean or one that is more extreme UNDER THE NULL HYPOTHESIS

For these mutually exclusive events, which rule is used?1. Player 1 gets 1 and P2 gets 1.2. Player 1 gets 2 and P2 gets 13. Player 1 gets 3 and P2 gets 1 
For exlusive events, the addition rule is used.in this case:P(1,1 or 2,1 or 3,1) = P(1,1) + P(2,1) + P(3,1)

Standard error represented as: 
SE = strd dev/ sq rt of n

mean is 10. sd is 2. what is score at z=+2 
14

Can hypothesis testing tell which of the hypotheses being tested is true? 
No. Hypothesis testing can only provide an educated guess about which one is likely to be true.

For which kind of variable is the binomial distribution used? 
discrete random variablesex. correct or not correct

smaller portion column in the normal distribution table refers to... 
area from z to pos infinity

What is type II error? 
Type II (Beta) is the prob of retaining Ho when it's false.

when p< alpha, what do we with the null? 
p< alpha, reject null

Ho is correctFail to reject the Ho 
assert difference is due to chance

If cards a drawn with replacement... 
Each card has an equal chance of being drawn.

___ refers to the normal distribution probability.____ of ____ is not a probability. 
An Area refers to the normal distribution probability.height of curve is not a probability.

How do you interconvert between the sm. portion and the p value? 
.081 is sm. portion8.1% is p value

Probability is determined as an ___ not a ___ 
Probability is determined as an area, not a height

8 grades are given for two different students. The instructor would like to know if the understand the material equally well. What are the null and alt hypoth? 
Ho= both understand mat'l equally wellH1= 1 of the students understood the mat'l better than the other

What kind of distribution would be used for height & weight measurements? 
Normal, because height and weight are continuous random variables.

A z = 1.2 means... 
the original x is below the mean by 1.2 standard deviations.

What do a series of normal curves with different means but the same strd deviation look like? 
different means = each line that vertically bisects each curve at its peak is at a different location.The same strd dev = same width

How is z useful in determining location? 
Z gives you a relative location in terms of how far your your number is above or below the mean

What terms can you use when referring to Ho? 
reject, retain, or fail to reject CANNOT EVER say accept. The use of accept is confined to the alternative hypothesis.

How calc the P(x and y)? 
P (x and y) = P(x y) * p(y)

How do you know which value to use in the alternative hypoth? 
Whichever number corresponds to results following the treatment or intervention.

Between what two scores do the middle 95% of sample means fall on a scale in which the mean is 100, std dev is 15, and sample size is 25? In this question, how do you determine the middle 95%? 
10095 = 5 percent, so there's five percent to be divided up between the two ends of the distribution.5/2 = 2.5Convert 2.5 to a propotion2.5/100 = .025If this will serve as the left end, make it negative (.025) and look up corresponding z in the sm portion.At the right end:95 + .025 = .975look in lg portion to find .975, then match this with a z value.

if p>alpha, what happens to the null hypoth? 
we will retain (fail to reject) Ho (null).

If you're not asked for a p value, you can do hypothesis testing with z alone. How? 
1. Your alpha level will determine the magnitude of your z critical, for alpha of .05, z=1.64, for alpha of .01 z is 2.33.2. The sign of your z crit is determined by a comparison of H1 with Ho. If H1 > Ho, then z crit is pos.3.If the calculated z is GREATER than z critical, then we reject the null. (This is diff than with p in which if calc p is LESS than .05 by the stat decion rule we reject the null).

8 grades of 2 students are given. Nicole gets higher grades six of the times.The instructor would like to know if they understand the material equally well. When calculating probabilites, what 3 P=# should be established? 
3 valuesP (when n=8 and p=1/2) =6P (when n=8 and p=1/2) =7P (when n=8 and p=1/2) =8wherep=1/2 was given in probn=total number of grades~I think that you start with P=6 in your calc of binomial probability values be/c its the highest number of superior grades obtained by either of the students. Once you've calc P=6,7,8 in the binomial way, add these 3 probs together and compare the result to .05 to determine retain or reject the null.

The p value is the tail area probability under which hypothesis? 
Tail area prob is the null.The large area that remains after you subtract away the tiny sliver of the p is the probability of the alternative probability, but this is NOT considered a p value.

If you don't have independent events, what is the rule that you MUST use? 
P(A and B) = P(AB)*P(B)or P(A and B) = P(BA) *P(A)

If A and B are independent events, what can we say about P(A B)? 
If A and B are indep, then:P(AB) = P(A)

for H1P(x bar > x bar observed)Will this calc produce a p value? 
No this is not a tail area, so it's not a p value

P = 0.2What does this mean in terms of a coin toss? 
P= 0.2 means that each time there's a 20% chance of heads

For a set of 10 probs, find the sm. # of items that a student has to do correctly to demonstrate that he is not doing them by sheer guessing? For this prob, what are the null and alt hypoth? 
Ho=student is doing the probs by guessingH1 = student is not doing the prob by guessing

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