Test 2 Flashcards
What is a normal distribution?
A theoretical distribution of values, also called bell curve
Why is a normal distribution theoretical?
because its frequency distribution is derived from a mathematical formula and not the observations of real data
What are some features of a normal distrbution?
the left and right tails continue to infinity and do not touch x axis, its unimodal and symmetrical
Why are normal distributions important?
many variables are thought to be noramlly distributed in the population (height, IQ), most inferential statistics assume normality, you can determine the proportion of scores in a normal distribution that are associated with any given score
What is the standard normal distribtuion?
aka z distribution, normal distribution of z scores, same features of normal distribution but mean is 0 and std is 1
What is the difference between standard normal distributions and normal distributions?
standard normal is distribution of z scores and normal is distribution of any scores
What is the 68-95-99.7 rule?
in a normal distribution, 68% of scores fall within 1 std, 95 within 2, and 99.7 within 3
If you wanted to find the z score in a standard normal distribution that separates the top 10 percent from the rest, how would you?
find 0.1000 in the column for proportion of tail or 0.9000 in column for proportion in body, look at corresonding z score
What are the two requirements for a random sample?
each individual has an equal chance of being selected, and if more than one individual is selected, the probabilities must stay constant for all selections
What is sampling with replacement?
when a subject is picked they are put back into the population before they pick again
what are the four steps of hypothesis testing?
state hypothesis and alpha level, lcoate the critical region, compute the test statistic, make a decision
How do you find the standard error of M?
std/sqrt of n
How do you find z value using standard distribution of mean?
z = M - m/std/sqrt of n
How would you find the probability of a z score falling between 0.5 and 1?
find proportion of body for 0.5 and subtract proportion of tail for 1
What is a type 1 error?
rejecting the null hypothesis when you shouldn’t (it was true but still got rejected)
What is a type 2 error?
failing to reject the null hypothesis when you should
How does increasing the alpha level from 0.01 to 0.05 affect the power of hypothesis?
increases it
How does changing from a 1 tailed test to a 2 tailed test change the power of the hypothesis?
decreases power if the effect is in the predicted direction
If p is less than a we ?
reject the null
If p is greater than or equal to a we ?
fail to reject the null
When is a t statistic used instead of a z statistic used in a hypothesis test?
when population standard deviation is unknown
it uses the sample deviation or variane instead
Why are t distributions flatter and more spread out than normal distributions?
because they are more variable since we do not know the population variance
What is an independent measures study?
uses a separate sample for each of the treatments or populations being
compared
How do you calculate the pooled variance given SS= 1740 and SS= 1620, and n=15?
- find sample variance for each
- s^2 = 1740/15-1 =124.29
- s^2 = 1620/15-1 = 115.71 - find the pooled variance
s^2 x df + s^2 x df/ n + n -2
(124.29 x 14) + (115.71 x 14) / 15 + 15 - 2
What formula can be used to calculate the estimated standard error for the sample mean difference?
SEdiff = sqrt(pooled variance/n + pooled variance/n)
What is the formula for sample variance?
s^2 = SS/n-1
What are non parametric tests?
make few if any assumptions about the populations from which the data are
obtained, any scale of measurement is acceptable
How to calculate expected frequencies?
multiply the two together and divide by n
What is the difference between the chi square goodness of fit test and the test for independence?
goodness of fit addresses only one nominal variable, independence addressses two nominal variables
What are some examples of parametric tests?
pearsons correlation, one sample t test
What are some examples of non parametric tests?
chi square, spearmann rank correlation
How do you calculate degrees of freedom for a pearson correlation test?
df = n - 2
How do you calculate r for pearson correlation?
r = SP/ sqrt(SSxSSy)
WHat does SP mean in r formula?
measures how x and y covary, equal to the summation of (X-Mx) x (Y - My)
How do you find SSx and SSY in r formula?
SSx is summation of squared deviations (X-Mx) SSy is same but for Y variable and My
When do you use pearson correlation?
linear relationship, both variables are interval/ratio
