ch 8 quizes and post tests STATS
population standard deviation
SE
Imagine two studies that are identical in every respect except the size of their samples. Sample A has an effect size of d = .40 and p-value of .001. Sample B also has an effect size of d = .40 but a p-value of .10. Which sample likely had the larger sample size? Sample B They are the same Cannot be determined without additional information Sample A
Sample A
type 2 error
- false negative - occurs when the null hyp is false ... that there really is an effect (soemthing going on) but you dont reject it. - only happens when the null hyp is NOT rejected. - telling a person that they dont have stage 4 cancer when they really do have stage 4 cancer. -
p values and sample size
- for the same effect size, a larger n will have a smaller more statistically significant p value for the same n a larger effect size will have a smaller p-value
intro into hypothesis testing
- it assumes nothing is happeneing (falsafiability) - it calculates the probabilty from 0-1 which corresponds to 0% to 100% of the observed results occuring if random quirkiness is the only explanation - it can provide a basic fr yes/no decision making and diagnosis
Which level of alpha for a hypothesis test has the lowest risk of a Type I error? .01 .05 .10 Cannot be determined without additional information
.01
When choosing a level of alpha for a hypothesis test, unless you have a compelling reason to do otherwise, you should use... .01 .10 0.50 .05
0.05 this is the false positive rate, the type 1 error rate. the 0.5 is very strongly engrained. you use this unless you hvae some strong reason to do seomthing else.
•For the same effect size, a larger n will have a (BLANK), more statistically (BLANK) p-value.
1) SMALLER more statistically significant p value
1.If a researcher wants to test whether an experimental group is different from the general population, then he/she would test . . . A.the hypothesis that the experimental group has a higher score than the population B.the hypothesis that the experimental group has a lower score than the population C.the null hypothesis of no difference between the group and the population D.whether her sample was representative
C
2.What does it mean when the result of a z-test is called "statistically significant"? A.The alternate hypothesis has been proven true B.The null hypothesis has been proven false C.The alpha value was greater than the p-value D.The results can be generalized to other populations
C
If a researcher is using an alpha of .05 for a z-test and gets an observed (or test) p-value of .23, then the researcher should... use a one-tailed test instead. reject the null hypothesis. retain (i.e., fail to reject) the null hypothesis. change the alpha to a larger value.
retain (i.e., fail to reject) the null hypothesis. what you are saying is (you hae hte %5 of the null distribution marked in red. a lot of the null distribution--- you have 23% of getting an answer in the null hypothesis range. that is too big. it needs to be less than 5% to suspect that something is going on.
Imagine two studies that are identical in every respect except the size of their samples. Sample A has an effect size of d = .20 and a p-value of .03. Sample B has an effect size of d = .20 and a p-value of .005. Which sample likely had the smaller sample size?
sample A sample A and B have the same effect size. the peaks are the same distance. the smallest sample is at the top. the bigger the sample the smaller the SE. you get this effect, you get less and less overlap. B has a value of 0.005. b value is much smaller and its overlap. which means that B must have a larger sample. A has the smaller sample.
directional (one tailed) hypothesis
direction is one that specifies whether the sample mean (or mean of the population from whih the sample is drawn) is expected to be one just one side of the comparison population's mean.
As n goes up, β goes ... BLANK
down because the standard errors get smaller and there is less overlap
the alt hyp
expirimental hyp. HA. something is going on for example all group means are not ewual and all correlations are not zero.
type 1 error
false positive - nothing is really happening .. that the null hyp is true... - but igen the peculiarities of the data, the researcher concludes that something is happening and rejects the null hyp. - charging an innocent person
as the alpha region goes up... beta goes .. BLANK
goes down
AS THE effect size goes up... the beta region .... BLANK
goes down.
retaining the null hyp
happens when your data doesnt suggest there is a statistical effect
rejecting the null
happens when your data suggest that there is a statically significant effect size that has a low probabilty of happening by chance.
interpreting cohends d
if it is positive, that means that the frist groups mean was higher than the second groups mean. if d is negative, then that means that the first groups mean is lower than the second groups mean. it isnt affected by sample sizes.
point estimates
in which we simply substituted the sample statistic for the population parameter, as thats the single most likely value from the sample
confidence interval
in which we were able to specify a likely range of possible values for the population parameter
when the sample size increases the z-score ..
increases
when sample size increases, the p-value ....
increases.
Directional, one-tailed test,
where you looking for higher scores: +1.645 That is, if you calculated value of z is higher than +1.645 (and it doesn't matter if it is lower than that), then you would reject the null hypothesis and conclude that the sample came from a population whose mean was significantly higher than the mean of the comparison population In each case, these critical values represent the cutoff point that separates 95% of the z-distribution - the middle 95% for a two-tailed test and the lowest or highest 95% for the one-tailed tests - from the remaining 5% of the z-distribution. As such, these represent the probability values of p < .05, which is a common cutoff. Any z-test with p-value less than .05 (e.g., p = .02 or p = .0001, etc.) would be considered statistically significant.
Directional, one-tailed test,
where you looking for lower scores: −1.645 That is, if you calculated value of z is lower than −1.645 (and it doesn't matter if it is higher than that), then you would reject the null hypothesis and conclude that the sample came from a population whose mean was significantly lower than the mean of the comparison population
If a researcher used a one-sample z-test to determine whether an experimental group was different from a general population, what she would actually be testing is... whether their standard errors were different. whether their distribution had any overlap whether their means are different. whether their distributions had the same shape.
whether their means are different.
WHAT TERM IS THIS: often abbreviated H1 or HA, which is the hypothesis that something is going on: for example, all groups means are not equal and all correlations are not zero.
•The alternative hypothesis, also called the "alternate hypothesis"ix or "experimental hypothesis,"
3.A Type I error occurs when . . . A.the sample data lead us to reject a null hypothesis that is true B.the sample is too small for significance testing C.the sample data lead us to retain (i.e., fail to reject) a null hypothesis that is false D.the sample data are biased in a systematic way
A
the null hyp
Ho. it is the hyp that nothing is going on. for example, all group means are equal and all correlations are zero
5.If a researcher is using an alpha of .05 for a z-test and gets an observed (or test) p-value of .23, then the researcher should . . . A.reject the null hypothesis B.retain (i.e., fail to reject) the null hypothesis C.change the alpha to a larger value D.use a one-tailed test instead
b
If a sample's mean really is different from the comparison population's mean, then what is the easiest way to make sure that the null hypothesis would be rejected? Getting as uniform a sample as possible Getting as representative a sample as possible Getting as large a sample as possible Getting as varied a sample as possible
Getting as large a sample as possible
if the sample's population is expected to have a higher mean
H0: µS ≤ µC
and the corresponding alternative hypothesis, which is the one that we are interested in or expecting, would be:
HA: µS > µC
If a research conducts a z-test and does not reject the null hypothesis, then... it is not appropriate to calculate an effect size. the researcher must gather new data. the researcher has proven that the null hypothesis is true. None of the other choices is correct.
None of the other choices is correct. we cant say for sure that there is zero probability that it comes from the alt or it must come from the null.. it could come from either one... null or hyp . a) no you always calculate an effect size that is a good thing to do . the fact that the z-test is or is not is satistically irrelevant b) thats if you made a big mistake, thats for replecation. failing to reject the null hyp isnt a mistake c) we dont PROVE that things are true.. we can say things are likely to happen but we dont PROVE
4.A Type II error occurs when . . . A.the sample data lead us to retain (i.e., fail to reject) a null hypothesis that is false B.the sample data lead us to reject a null hypothesis that is true C.the sample is too small for significance testing D.the sample data are biased in a systematic way
a
If a person's blood sample tests positive for a disease when, in fact, the person does not have the disease, then... a Type II error has occurred. a Type I error has occurred. a testing error has been made. the procedure must not have been conducted correctly.
a Type I error has occurred.
A Type I error is also called... a false negative a true positive a true negative a false positive
a false positive
effect size
a general measure of group differences. such as the size of the difference between the means of two groups. degree of association between two or more varaibles. COHENDS D is the effect size here
cohends d
a standardized measure of the difference between two sample means. how far apart means are in unites of standard deviations.
When the mean of the population that a sample comes from does not differ from the general population but the sample mean is nonetheless significantly different from the general population, then... the researcher should gather new data. a Type I error has occurred. a sampling error has been made. a Type II error has occurred.
a type 1 error has occured. the mean of the sample population does not differ from the general population. that means that the null hyp is TRUE. but the sample mean is different than the general population then a type 1 eror has occured. (if you look at the graph) (even tho its rare that you would get a score from the %5 of the sample mean... its STILL POSSIBLE.
the logic of hyp testing
after making an assumption such as " the notre dame football team is expected to win 90% of their games"---- hypothesis tests then assume that any difference between hypothesized population parameter and the observed sample statistic is due solely to random sampling error. then it estimates the probabilty of obtaining the ovserved sample statisic through random sampling error from the hypothesized population. if the probabilty is TOO low. the null is rejected . of the probability is higher than that the nill is not rejected. `
If a researcher believes that the null hypothesis is false and wants to have the greatest chance of rejecting it with their study, then which of the following would make it more likely that the null hypothesis would be rejected? Increasing n Increasing the critical value Decreasing the effect size Decreasing n
increasing n the larger the sample... the smaller the NULL and so it is more lieky to be rejected. changing the critical values if you decrease the critical values that would give you more statistical power, but it would decrease type 2 errors and false positives. thats not good decrease the effect size, makes it harder to find what you are looking for.
When calculating an effect size for the z-test... the sampel size must be large (n > 100). it is most common to use Cohen's d. z must have an absoute value greater than 2. the sample data must be normally distributed.
it is most common to use Cohen's d.
falsifiability
it is much easier to prove that there is an exception to a rile (all you have to do is ) find the single exception. than to rpove that there are no exceptions to a rule. (which would require that you test every single possibility which is usually impossible or impractical.
In a two-tailed or non-directional test, if the critical value has a greater absolute value than the observed (or test) value does, the the null hypothesis... must be replaced with a one-tailed or directional hypothesis. is not rejected (i.e., retained). is rejected. is proven false
it is not rejected (i.e. retained). the null hypthesis is not rejected. if the observed value is less than the critical value... then the hypothesis is NOT rejected.
one tailed hypothesis
it is only concerned about whether the sample's mean falls into one of the tails in the sampling distribution
A researcher who wants to use a z-test to compare a sample mean to a population mean must first... choose measures that yield ratio level data. delete any outliers from the sample data. know the population standard deviation. recruit a diverse sample of participants.
know the population standard deviation -- you have to know the population SD in order to caclulate the z-test. a) outliers can be a problem but you dont just simply delete them. that doesnt ahve anyhting to do with the aplicability of the z-test b) you should have something that yeilds interval or ration level D) that has nothing to do wtih the relevance of the z-test.
In order to compute a one-sample z-test you must... first know whether the sample mean is different from the population mean. have a large sample (n > 100). know the population standard deviation. calculate the sample standard deviation.
know the population standard deviation.
Imagine that a researcher is interested in whether residents in his local area have higher levels of well-being than the national average. What would be an appropriate alternate hypothesis for a one-tailed or directional z-test for this test? local residents average < national average local residents average = national average None of these choices are appropriate local residents average > national average
local residents average = national average remember when you are doing hypothesis testing, they come in pairs. look at the equation for the hyp and null hyp. the alternative hyp is the one we are usually interested in. whether the mean for their local group is higher for their national group. it is MU because we are talking about a national (population group) the alternative says greater than.... bc the hypothesis need ot be mutually exclusive and comprehensive the null needs to be less than and equal to.
non-direction two tailed hypothesis
one that asks whether the sample mean or more accuratley, the mean of the population from which is the sample is drawn is DIFFERENT or HIGHER or LOWER than is the comparisons populations mean. this is called a two tailed hyp. bc it is concerned whether the samples means falls in either of the tails in teh sampling distribution.
beta region
part of the alternative distribution for the alt hypothesis
alpha region
region of rejection - increases risk of type 1 error rates.
If a researcher is using an critical value of \pm ± 1.96 for a z-test and gets an observed z (i.e., test value) of +0.55 for a sample of n = 40, then the researcher should... retain (i.e., fail to reject) the null hypothesis. reject the null hypothesis. reach no conclusion without additional data. reject the alternative hypothesis.
retain (i.e., fail to reject) the null hypothesis.
If a researcher is using an critical value of ±1.96 for a z-test and gets an observed (or test) z of -1.73, then the researcher should... retain (i.e., fail to reject) the null hypothesis. change the critical value to a smaller value. use a one-tailed test instead. reject the null hypothesis.
retain (i.e., fail to reject) the null hypothesis. we set up this decision criteria that it has to be 1.96 SE. the sample mean has to be 1.96 SE away from the null distribution. the one that we have is 1.73 SE away from the null hyp. because it doesnt get to that point, we say "nothing is going on" and we reject the null hyp.
Imagine two studies that are identical in every respect except their effect sizes. Sample A has a sample size of n = 80 and a p-value of .01. Sample B has a sample size of n = 80 and a p-value of .10. Which sample likely had the larger effect size? Cannot be determined without additional information They are the same Sample A Sample B
sample a look at the z-score formula. the effect size is going to have a lot to do with the difference of the means... the p-value is going to change. the p-value is going to work into z. and the effect size is going to be bigger or smaller depending on that particular distance. the bigger the distance bweteen those means, the larger the z-score is, and also the smaller the p-value is. bigger sample size, smaller p-value
p value
short for probability value . - the probabily of the obverved value for a statistic. (the sampling mean) arising through random meaniningless variatiopn when the true pop effect size is 0. - calcuatling a test stat - finding where that test stat falls in the relevant distribution - finding the proportion of the distribution that is at least that far from 0
•For the same n, a larger effect size will have a BLANK p-value.
smaller
What does it mean when the result of a z-test is called "statistically significant"? The null hypothesis has been proven false The alpha value was greater than the p-value The alternate hypothesis has been proven true The results can be generalized to other populations
the alpha value was greater than the p-value. of these 4 choices its the only one thats acuracte. A and B are not accurate because we are dealing with a problematic excersize. you dont want to talk about proving anyhting true. you can only do that if you find something that is true 100% of the time and that doesnt happen with behavioral statistics. D- how you gathered your data and not whether they are statisticly sifnificant.
WHAT IS THIS TERM: often abbreviated H0, which is the hypothesis that nothing is going on: for example, all groups means are equal and all correlations are zero.viii
the null hyp
If a researcher wants to test whether an experimental group is different from the general population, the she would test... the hypothesis that the experimental group has a lower score than the population. whether her sample was representative. the null hypothesis of no difference between the group and the population. the hypothesis that the experimental group has a higher score than the population.
the null hypothesis of no difference between the group and the population. we test the null hypothesis to see if we have data that would be an exception to it. its very hard to prove B and C, but its easier to prove there are exceptions vs proving that there ARENT exceptions.
If you draw a picture of the null distribution with the critical values and regions of rejection marked, then the alpha level is represented by... the proportion of the distribution in the regions of rejection. the proportion of the distribution between the critical values. the location of the observed sample values. the height of the distribution at the critical values.
the proportion of the distribution in the regions of rejection. it is the 2 tails on the graph. the null distribution "its the range of values that can happen through random error when nothing is happening" its possible to get very high and very low value.. but we set those off as being unusual and more likely to be due to something else then just likely to be due to random error.
The z-test is appropriate when... the data consist of nominal variables. the researcher knows the population mean and variance/standard deviation the data distribution is symmetrical. the researcher needs to estimate the population variance/standard deviation
the researcher knows the population mean and variance/standard deviation you can tell from the formula its simply a Z-score. you have to subtract the population mean (that is something you need to be given.) in the formula, there is the SE, you have to already have that information.
If a researcher is using alpha = .01 and gets a p-value for the z-test of p = .005, then... the researcher should conclude that the results are unlikely to occur by chance if the null hypothesis is true. the researcher should conclude that the results are likely to occur by chance if the null hypothesis is true. the researcher has proven that the alternative hypothesis is true. the researcher has proven that the null hypothesis is false.
the researcher should conclude that the results are unlikely to occur by chance if the null hypothesis is true.
If a researcher is using alpha = .05 and gets a p-value for the z-test of p = .02, then... the results are likely to occur by chance if the null hypothesis is true. the results are unlikely to occur by chance if the null hypothesis is true. this proves that the null hypothesis is false. Cohen's d = alpha/p = .05/.02 = 2.5
the results are likely to occur by chance if the null hypothesis is true. look at the graph. the null distribution is on the left which means nothing is happening. and the alt hyp is on the right which means which sample values are possible from the alternative distribution. yes it is possible for something like this to happen in the null distribution. on the other hand, the change of that occuring in the alternative distribution is more likely to occur. its more likely to occure through some other means. you can get a value of x.. its more liekly to occure iwth some other means. the p-value tells us how often you would get a score that big if hte null hyp is true. (its just 2% of the time) B) just needs to be flipped around the other direction c) we arent in the business of proving things, the data is either inconsistent or consistent. d) the c-hends d isnt right bc thats not even the formula for d.
A Type I error occurs when... the sample data lead us to retain (i.e., fail to reject) a null hypothesis that is false. the sample data lead us to reject a null hypothesis that is true. the sample is too small for significance testing. the sample data are biased in a systematic way.
the sample data lead us to reject a null hypothesis that is true. it is a false positive. the idea here is that the null hyp is true, (look at the graph) you are looling at the top 5% of the distribution on the right.... on the left the rest of the data is 95% there are more alternative meanings with that bc its a more likely outcome. BUT the value that we have for X (5%) is still a possiblilty of happening,... we will reject the null hypothesis. it is a sampling error. a sample with a really high mean.
A Type II error occurs when... the sample data are biased in a systematic way. the sample data lead us to reject a null hypothesis that is true. the sample data lead us to retain (i.e., fail to reject) a null hypothesis that is false. the sample is too small for significance testing.
the sample data lead us to retain (i.e., fail to reject) a null hypothesis that is false. what that is a false negative, meaning that there is really something going on and we should have rejected it, but our sample data didnt lead us to that condition. (the X) is the the left of the null hyp, meaning it is a random value and we are going to accept it as a random varaition. (look at the graph.) bc its on the low end, we would assume that it represents no varaiation and it does. .. it just happened to be wrong due to sampling error.
If a researcher is comparing a sample mean to a population mean and gets Cohen's d = -2.0, this means that... a mistake was made because Cohen's d cannot be negative. the sample mean is two standard deviations below the population mean. the effect is statistically significant. the sample mean is two standard errors away from the population mean.
the sample mean is two standard errors away from the population mean.--- a cohens d of -2.0 means that the sample mean is 2 standard deviation below the population mean. a) woudl be true if we found the z-score and it would be -2.0 b) if we were doing a z-test and were using a 2 tailed or non directional test with an aphla of 5... then that would be true.. but thats not what we are asking about. c) no all that means is that the sample mean is bellow the population mean,... no.
When calculating an effect size for the z-test... you must first check for homogeneity of variance. you must use the population standard error. the sample size is irrelevant. the alpha values must be incorporated.
the sample size is irrelevant. look at the formula for Cohens D. that is the major difference between Cohens D and the Z-score. is the fact that Cohens d is NOT AFFECTED BY SAMPLE size in how it treats the standard deviation.
