biostats test 3

critical values for common confidence levels: confidence level 90% so critical value z* is ________.

1.645

critical values for common confidence levels: confidence level 95% so critical value z* is ________.

1.96

For the Wald confidence interval, the sample is considered large enough only if np-hat >/= ____ and n(1 - phat) >/= ____.

15; 15

The __________ is a statement that the parameter has a value that is somehow different from the null hypothesis. If you are conducting a study and want to use a hypothesis test to support your claim, the claim must be worded so that it becomes the __________.

alternative hypothesis; alternative hypothesis

_________ studies are more convincing than one-sample investigations. Comparative inference is more _________ than one-sample inference. A common design uses _________ procedures to compare two groups.

comparative; common; one-sample

The mean is fixed...either it falls in the confidence interval or it does not. Never talk about the probability that mean lies in the interval. Instead talk about your _________ that the interval covers the true mean.

confidence

provides a range of reasonable values that are intended to contain the parameter of interest and provides a measure of our confidence that the parameter of interest is actually contained in the interval

confidence interval

The _________ tells you how many standard deviations above and below a sample mean you must go to make an interval that contains the population mean in a proportion (1 - critical value) of all samples.

critical value

A _________ is a point on the test distribution that marks off specified areas that are related to alpha .It is used to create confidence intervals with a specified confidence level. Used to decide whether to reject the null at the alpha level. If the absolute value of the test statistic is greater than the critical value (t*), reject the null at the alpha level

critical value (t*)

Values of distributions (like z*) that mark off specified areas are called __________ of the distribution.

critical values

Values of distributions (like t*) that mark off the specified areas are called __________ of the distribution. The _________ tells you how many standard deviations above and below a sample mean you must go to make an interval that contains the population mean in a proportion (1 - alpha) of all samples.

critical values; critical value

Under a _________, all subjects receive both treatments in random order. In a crossover design, subjects are independently and randomly assigned to one of two groups. Those assigned to group 1 receive treatment 1 first followed by a washout period, then receive treatment 2. Those assigned to group 2 receive treatment 2 first followed by a washout period, then receive treatment 1.

crossover design

If the p-value is greater than the critical value, then _________ the null hypothesis and we say that the data are ________ at the significance value level. Failing to find evidence against the null only means that the data in this sample are ________ with the null, not that we have clear evidence that the null is true.

fail to reject; not statistically significant; consistent

When making inference about mean, degrees of freedom equals _________. (we lose ____ df by estimating sample mean)

n - 1; 1

In a ________ design, each subject/observation is matched to another subject/observation.

paired

With independent samples t tests, we compare the populations by doing inference about the population _________ between the population means.

parameter

Interested in the unknown proportion p of a populationthat has some outcome. Call the outcome of interest a "_________." The statistic that estimates the parameter p is the __________ (read as "p-hat").

success; sample proportion

The sample proportion (p-hat) is equal to the number of _________ in the sample divided by the ________ number of individuals in the sample.

successes; total

Complete, journal-style conclusion for paired t-test for a significant result includes: population to which inferences may be made. Causal inferences, if any (randomized experiments). Evidence upon which the conclusion is based (test statistic, df, p-value). Direction of effect (whether group assignment increases or decreases effect). Magnitude of effect (how much does group assignment increase or decrease effect...sample mean). Uncertainty estimatefor the point estimate (estimated standard error of the statistic or confidence interval for the parameter).

.

This Wald approximation is very common, but can yield unsatisfactory results, especially when p is near ____ or ____ or when n is _______. Overestimates the precision of estimating p...too "________." If attempting to make a 95% CI, the interval may include p ______ than 95% of the time. The calculated confidence interval is always symmetrical around _____. May result in a lower limit for the CI that is less than 0 or an upper limit for the CI that is greater than 1.

0; 1; small; liberal; less; p-hat

Requirements for proportion z test: The sample can be regarded as a simple random sample. The conditions for a binomial distribution are satisfied. The conditions np-hat >/= _____ and n(1-p-hat) >/= _____ are both satisfied.

10; 10

critical values for common confidence levels: confidence level 99% so critical value z* is ________.

2.576

For two-sample t test (unequal variances), the requirements that must be satisfied are: Both samples can regarded as Simple Random Samples (SRS) from two distinct and independent populations. AND either both samples come from populations having normal distributions and/or n1 >/= _____ and n2 >/= _____.

30; 30

The _________ confidence interval makes avery simple adjustment to the Wald interval, but works almost as well as the Wilson interval. This method works well as long as n >/= _____ and the confidence level C is at least _____%. Other requirements: the sample can be treated as a simple random sample and the conditions for a binomial distribution are satisfied.

Agresti-Coull; 10; 90

confidence interval for p for large-sample size

Wald

In Stata, if a confidence interval for a population proportion results in a: a lower bound less than 0 or an upper bound greater than 1, then a warning is provided: The "interval was clipped at the lower endpoint." The "interval was clipped at the upper endpoint." The _________ is guaranteedto yield both upper an lower bounds in the appropriate range.

Wilson CI

The ________ Interval (sometimes called the _______ interval) is a much better choice over the Wald interval. This method works well for samples as small as n=_____.

Wilson; score; 10

When the null hypothesis is not rejected, one should NOT say that the null hypothesis is ________. We may have committed an error.

accepted

When the null hypothesis is rejected, one should NOT say that the alternative hypothesis is ________. We may have committed an error.

accepted

If we find sufficient evidence that the null is false, then its complement must be true. For this reason, we always make the thing that we want to show is true to be the __________.

alternative hypothesis

Examples of paired data: some patients ________ and ________ treatment; _________ used in genetic studies; patients matched by ________, ________, and ________.

before; after; identical twins; age; race; gender

A _________ variable has only two possible outcomes: X= 1 if a person has a cold, and X=0 if a person doesn't have a cold.

binary (dichotomous)

Requirements for inference about p: The sample can be treated as a simple random sample. The conditions for a _________ are satisfied. The _________ must be big enough.

binomial distribution; sample size

The point estimate of the parameter will always be the ________ of a confidence interval. A CI for a population mean will always be centered on the _________. _________ the sample size will lead to a wider interval, all else held constant. ________ the confidence level will lead to a wider interval, all else held constant. ________ the standard deviation will lead to a wider interval, all else held constant.

center; sample mean; decreasing; increasing; increasing

Significance levels are ________, not ________.

chosen; calculated

measure the amount of information available in the data that can be used to estimate the standard deviation

degrees of freedom

As the __________ increases, the t distribution becomes increasingly like the standard normal distribution. s estimates standard deviation more accurately as the __________ increases.

degrees of freedom; sample size

To compare the responses to the two groups in a paired design, find the _________ between the responses within each pair. Then apply the _________ t procedures to these differences.

difference; one-sample

Using the rare event rule, we test a claim by analyzing sample data in an attempt to distinguish between results that can _________ by chance and results that are __________ to occur by chance. If we actually observe results that are highly unlikely, either: A _________ has indeed occurred, or the underlying _________ is not true.

easily occur; highly unlikely; rare event; assumption

There are two different types of two-sample t-tests, depending on how the standard error is calculated. The "_________" or "_________" option, assumes that the two populations have the same variance. The "__________" option makes no assumption regarding the equivalence of the population variances.

equal variances; pooled; unequal variances

Most confidence intervals take the form: __________ +/- __________. The _________ shows how accurate we believe our guess is, based on the variability of the estimate (standard error).›The _________ of a confidence interval refers to the success rate of the method in capturing the parameter of interest.

estimate; margin of error; margin of error; confidence level

There is a mathematical equivalence between confidence intervals and hypothesis tests with __________ alternative hypotheses. You will _________ the null at the significance level is the hypothesized mean in the null is contained in the confidence interval. You will _________ the null at the significance level if the hypothesized mean in the null is not in the confidence interval.

fail to reject; reject

There is a mathematical equivalence between confidence intervals and hypothesis tests with two-sided alternative hypotheses. For a confidence interval: You will _________ the null at the significance level if the hypothesize mean in the null is contained in the CI. You will _________ the null at the significance level if the hypothesized mean in the null is not in the CI.

fail to reject; reject

t* is a critical value for the t distribution. It depends on degrees of freedom, df. Its value is fixed once you choose alpha (either the significance or confidence level). t* is the number on the borderline separating sample statistics that are likely to occur from those that are unlikely to occur. t* is the standard for "_________" for the test statistic to be able to reject the null.

far enough

For paired t-test hypotheses, the null hypothesis says that _________ has no effect on the outcome of interest.

group membership

The goal of a _________ is to assess the evidence provided by data about some claim concerning a population parameter.

hypothesis test

An _________, often simply called a _________, uses independent samples. Two samples are _________ if the data points in one sample are unrelated to the data points in the second sample.

independent samples t test; two-sample t test; independent

The number of successes X is a binomial random variable when: There are a fixed number of ________ trials. There are two possible _________ (success and failure) for each trial. The probability of _________ is the same for each trial.

independent; outcomes; success

It turns out that when the sample size, n, is very ________, you can use a z-score to construct a confidence interval even when you are estimating standard deviation with s.

large

The binomial distribution of X can be approximated by a Normal distribution. When n is ________, the distribution of X is approximately normal. Use the normal approximation if n is so big that np >/= _____ and n(1-p) >/= _____.

large; 10; 10

________ values of the test statistic show that the data are far from what we would expect if the null hypothesis was true. ________ values of the test statistic show that the data are close to what we would expect if the null hypothesis was true.

large; small

There are three possible choices of alternative hypotheses to consider...the parameter is: _________ than the null hypothesis value, _________ than the null hypothesis value, or _________ from the null hypothesis value (smaller or larger).

larger; smaller; different

Paired data typically occur out of one of the following three scenarios: _________, _________, or _________.

longitudinal designs; matched-pair designs; crossover designs

Under a _________, the same group of subjects is followed over time. The paired data is usually from the same subject before and after some treatment is applied.

longitudinal study design

When planning a study, we often want to choose a sample size that will allow us to estimate the parameter within a given _________.

margin of error

Under a _________, subjects are matched in pairs in such a way that the two members of a pair share similar characteristics, such as age, gender, disease severity, etc. One member of each pair is randomly assigned to one group, and the other member is assigned to the other group.

matched-pair design

The parameter mean in a paired t procedure is the _________ in the responses to the two groups within pairs of subjects in the entire population.

mean difference

With two-sample t tests (independent samples), we want to test whether the data contained in the samples provides enough evidence to suggest that there is a difference between the ________ of the two populations.

means

For a confidence interval: Any value of z (test statistic) that is in the _________ region, between -z* and z*, would result in a p-value ________ than alpha, and the null will not be rejected at the significance level. Any value of z (test statistic) that is in the _________ region, less than -z* or greater than z*, would result in a p-value ________ than or equal to alpha, and the null will be rejected at the significance level.

non-rejection; greater; rejection; less

For a confidence interval, any value of t (test statistic) that is in the __________ region, between -t* and t*, would result in a p-value greater than alpha, and the null will _________ at the alpha significance level. Any value of t (test statistic) that is in the __________ region, less than -t* or greater than t*, would result in a p-value less than or equal to alpha, and the null will _________ at the alpha significance level.

non-rejection; not be rejected; rejection; be rejected

The condition that the variable be normally distributed is typical for most statistical procedures. By the CLT, we know that the sampling distribution of the sample mean will be approximately normal if at least one of the following is true: the observations in the population are _________ or n >/= _______.

normally; 40

Basic idea of hypothesis testing: if an event happens that would rarely happen if a claim was true, then the fact that it happened is good evidence that the claim is _________.

not true

The claim tested by a significance test is called the __________. The null hypothesis is a statement that the value of the population parameter is ________ to some claimed value. The claim is usually an __________. Hypothesis tests are designed to assess the strength of evidence against the __________.

null hypothesis; equalaccepted belief; null hypothesis

Draw a SRS of size n from a large population having unknown mean. To test the hypothesis that the mean equals the null when standard deviation is not known, we must use the ________ t statistic which has a t distribution with df= _________. This is the _________ for the one-sample t test.

one-sample; n- 1; test statistic

The alternative hypothesis is _________ if it states that the parameter is larger than or smaller than the value hypothesized in the null hypothesis. The alternative hypothesis is _________ if it states that the parameter is simply different from the value hypothesized in the null hypothesis.

one-sided; two-sided

The null hypothesis should never ________ with the alternative hypothesis. They are intended to be set in such a way that one must be true and the other false. A researcher seeks evidence against the null hypothesis as a way of bolstering the alternative hypothesis.

overlap

A study that is too large is called __________. The fact that n is so big makes it likely that the null will still be rejected. Even if the difference is not a clinically significant difference, the test would indicate a statistically significant difference.

overpowered

The strength of the evidence against the null is quantified by a probability called a ________. The ________ is the likelihood that random chance could give you the results you got, or results even further from the null, if the null is actually true. The probability, assuming that null is true, that the _________ will take a value at least as extreme as that actually observed.

p-value; p-value; test statistic

95% confidence interval tells us that if we were to repeatedly make new estimates using exactly the same procedure (draw a new sample, calculate new estimates, and new confidence intervals), the 95% of the confidence intervals would contain the ___________.

population parameter

A full conclusion regarding parameter estimates should contain: _________ on which inferences are made (if possible), _________ estimate (including units of measurement), and an assessment of _________ (either the standard error of the mean or a confidence).

population; parameter; uncertainty

After selecting a sample, we know the responses for the individuals in the sample, but we usually take a sample to infer some conclusion about the __________. Since a different sample may lead to different conclusions, we can't know with certainty that our conclusions are correct. So, we use __________ to determine how trustworthy our conclusions are

population; statistical inference

A count of successes is only meaningful in the context of the total number of observations, so it is not useful for comparing results from different studies. Thus, the parameter of interest is the _________ of successes.

proportion

When working with binary variables, we are typically interested in the proportion of the subjects possessing a certain trait or characteristic. In this case, the parameter we are interested in estimating is not a population mean, but instead a population _________, denoted ______.

proportion; p

In order to understand a hypothesis test, it is important to remember the __________ that we discussed previously: If, under a given assumption, the probability of a particular observed event is exceptionally ________, we conclude that the assumption is probability not correct.

rare event rule; small

There are only two possible outcomes of a hypothesis test. _________: This means that there is significant evidence from the experiment that the null is false. So either, the alternative is true or we observed something really unlikely. _________: This means that there is not significant evidence from the experiment that the null is false. So either the null is true or the study is inconclusive.

reject the null; fail to reject the null

If the p-value </= critical value, ________ the null. If the p-value > critical value, ________ the null.

reject; fail to reject

If the p-value is </= the critical value, then ________ the null hypothesis, and we say that the data are _________ at the significance value level (meaning that assuming that the null hypothesis is true, what we observed is not likely to happen just by ________).

reject; statistically significant; chance

A confidence interval or hypothesis test is called _________ if the confidence level or p-value doesn't change very much when the procedure's requirements are violated. The t procedures are considered robust to most violations, unless the data are very _________ and the sample size is really _________ (less than 15).

robust; skewed; small

Since we don't know the standard deviation, we can estimate it using the __________. The estimated standard error of the sample mean is equal to __________.

sample standard deviation (s); s/square root of n

Requirements for T-based CI for mean: The population standard deviation is unknown, but the _________, _____, is known. Your sample can be regarded as a ___________ from the population. The observations from the population are normally distributed and/or the sample size is at least ______ (CLT holds).

sample standard deviation; s; simple random sample (SRS); 40

a measure of the acceptable risk of rejecting a true null hypothesis so we make it small

significance level (alpha)

There are fixed standards for p-values are called __________, and they are denoted by the Greek letter alpha. Significance levels are commonly used as standards for evidence against the ________. The significance level, alpha, is the probability of making the mistake of rejecting a true _________ (_________).

significance levels; null hypothesis; null hypothesis; type I error

The condition that the sample be a __________ is typical for most statistical procedures. If your data don't come from a probability sample or a randomized experiment, your conclusions may be challenged.

simple random sample (SRS)

________ p-values are evidence against the null hypothesis because they indicate that the observed result would be unlikely to occur if the null hypothesis was true. ________ p-values fail to provide evidence against the null hypothesis.

small; large

Since rejecting a true null hypothesis would constitute an error, we select a ________ value of the critical value in order to make the probability of rejecting a true null hypothesis ________.

small; small

the probability of rejecting the null hypothesis when, in fact, it should be rejected

statistical power

The value of _______ can be found the t-table (where degrees of freedom and confidence level correspond)

t*

lists critical values of t distributions

t-table

_____ distributions are a family of distributions with members sharing characteristics. Each member is identified by its __________. The __________ measure the amount of information available in the data that can be used to estimate standard deviation. Measure reliability of _____ as an estimate of standard deviation.

t; degrees of freedom (df); degrees of freedom; s

The density curves of the t distributions are similar to the standard normal distribution...they are symmetric, bell-shaped, and centered on 0. t distributions have more area in their ________ than the standard normal distribution. The broader ________ accommodate the additional uncertainty that comes from estimating standard deviation with s.

tails; tails

A _________ is a measure of how far the data diverge from the null hypothesis.

test statistic

Large values of the ________ show that the data are far from what we would expect if the null was true.

test statistic

The _________ can be used for determining whether there is significant evidence against the null hypothesis.

test statistic

It is more common to compare the means of __________ populations, where both population means are unknown, than it is to test claims about the mean of one population. Often, the two groups have received different treatments or undergone different exposures.

two different

You should always use a _________ alternative, unless you have a very good scientific reason to do otherwise.

two-sided

It is more difficult to reject a null hypothesis when you are using a _________ alternative. When you do reject a null hypothesis with a ________ alternative, it is more convincing than if you had used a _________ alternative.

two-sided; two-sided; one-sided

The error committed when a true null hypothesis is rejected is called a _________. The probability of committing a type I error is denoted by ________. Whenever we _________ a null hypothesis there is always the risk of a type I error.

type I error; alpha; reject

The _________ is the error committed when a false null hypothesis is NOT rejected. The probability of committing a type II error is denoted by _________. Whenever we _________ a null hypothesis there is always the risk of a type II error. We generally exercise no control over beta, although we know that in most practical situation it is ________ than alpha.

type II error; beta; fail to reject; larger

A study that is too small is called __________. The fact that n is so small makes it likely that the null will still NOT be rejected. Even if the difference is clinically significantly different, the test would indicate that there is NOT a statistically significance difference.

underpowered

The "__________" t procedures are almost always more accurate than the pooled procedures.

unequal variances

Since we are estimating the value of the population standard deviation with the sample standard deviation, a new source of uncertainty is introduced. Because of this additional uncertainty, we can't use a standard normal _____ distribution when making inferences anymore.

z