Alternative Questions for Chapters 8-10 Flashcards
What does it mean to reject the null hypothesis?
Implies that sample comes from a different population than null
What does retaining a null hypothesis tell?
Did not find sufficient evidence to reject it
What does retaining a null hypothesis not mean?
That null is true or even probably true
How do make the standard error formula unbiased?
Sx(bar)= sx / sq rt of n
What does estimating the standard deviation mean?
No longer assume that the sampling distribution will have all characteristics of a normal distribution
What are the similarities between the z and t distributions?
Symmetrical, unimodal, mean of 0
What are the differences between the z and t distributions?
T-distribution is more flat, t has a larger standard deviation, t has larger critical values
What does it mean that the t distribution has a larger critical value?
Sample mean has to be farther away from null to reject it
What does the degree of freedom represent?
Number of scores in a distribution that are completely free to vary
What does a single means t-test mean in regard to degree of freedom?
N-1 degrees of freedom
Is the procedure for hypothesis testing different for z-tests than t-tests?
No
What do we call it when we reject null after conducting a hypothesis test?
Result is significant
What is reason number 1 why statistical significance does mean importance?
Likelihood of obtaining significant result is largely influence by sample size
What is reason number 2 why statistical significance does mean importance?
Importance depends heavily on research context in which results are evaluated
What is another way to think about a sample mean?
Determine distance from the hypothesized value in terms of standard deviation of pop rather than standard error of sampling distribution
What happens when standard deviation is unknown?
Substitute our unbiased estimate of the sd for Hedge’s G
What are conclusions about hypothesis testing based on?
Probability not certainty
What is possible with all hypothesis testing?
That you have a perfect hypothesis and still arrive at the wrong answer
Which error type is more serious and why?
Type 1
What does changing the alpha do in a test?
Makes type 1 smaller while increasing type 2
What is the alpha value?
Criterion for how unlikely the result must be to reject null
What does the alpha value result mean?
if null is true likelihood of getting value in rejection region and therefore making type 1 error is also that value
What does changing the sample size do in a test?
Less change of making a type 2 error
What does changing the sample size in a test mean?
If null is not true you have better chance of rejecting It as the sample size gets bigger
What does changing the sample size mean?
affects error by altering standard error of mean
What do bigger samples provide in a test?
provide better estimates of the population mean so sampling distributions have smaller standards errors than distributions of smaller samples
What is power the probability of?
Finding significant difference when you perform your hypothesis test
What question are you asking yourself in post-hoc?
Given the way in which I have conducted this test, what is the likelihood that I would have found a significant difference is actually there?
What does post-hoc mean?
After a hypothesis test is performed
What are the four ways we determine the power of a z-test?
Value predicted by null, standard error of the mean for your hypothesis test, true mean of pop, alpha of the test
what are the factors that influence type 1 error?
significance level set for the hypothesis test, the sample size, and the effect size.
What are the factors the influence a type 2 error?
significance level, the sample size, the effect size, and the variance of the population
Under what circumstances do we use a z-test vs. a t-test?
Z-test: population parameters are known, sample size is large
T-test: population parameters are unknown, sample size is small
What makes calculating a t-test difference from a z-test?
t-test takes into account the degree of uncertainty that comes from estimating the population standard deviation from a sample.
How do you conduct a hypothesis test of a single means t-test?
state hypothesis, formulate an analysis plan, analyze sample data, interpret results
How do you calculate the effect size of a t-test?
This is calculated as the difference between the two means (or the mean difference) divided by the pooled standard deviation
How are null and alternative different from two sample tests (compared to single means)?
main difference lies in what you’re comparing: a single population mean to a specific value (single mean t-test) or the means of two populations to each other (two-sample t-test).
In a single means t-test what does the null and alternative typically state?
population mean is equal to a specified value, while the alternative hypothesis states that the population mean is different from that value
In a two sample t-test what does the null and alternative typically state?
null hypothesis is typically that the means of the two populations are equal, while the alternative hypothesis is that the means are not equal
What could the alternative alternatively state in a two sample t-test?
one mean is greater than or less than the other, depending on the question of interest
What is the sampling distribution of independent samples test?
distribution of the differences between the means of two independent samples
What is Hedge’s g?
measure of effect size, measure of the magnitude of the difference that is not dependent on the sample size
How do you calculate Hedge’s g?
calculated as the difference between the two means divided by the pooled standard deviation, but then multiplied by a correction factor
When is Hedge’s g particularly useful?
comparing the means of two groups
What are the statistical assumptions of independent samples t-tests?
independence of observations, normality, homogeneity of variance
What is independence of observations?
observations in each sample must be independent of each other
What is normality?
data in each sample should be approximately normally distributed
What is homogeneity of variance?
variances of the populations from which different samples are drawn are equal, spread or dispersion of scores around the mean is the same for all groups being compared
Why is homogeneity of variance important?
many statistical tests rely on it to give valid results
How to integrate various inferential statistics to consider the meaning and implications of a results?
consider the context, look for consistency, consider practical significance, think about implications
Researchers are testing the potential side effects of a new anti-depressive medication. They conduct a study in which half of the participants receive the experimental medication, while the other half receive a pre-existing medication. They want to make sure that they can detect any side effects that may exist. In other words…
Want to avoid making a type 2 error
Given the researchers concerns in question 6, what impact would changing the alpha level of the study from .05 to .01 have for their study?
Increase the chance of their concerns becoming real
When we have to estimate the population variance or standard deviation using a sample, we use the formula s^{2}=\frac{\sum \left ( X-\overline{X} \right )^{2}}{n-1} instead of s^{2}=\frac{\sum \left ( X-\overline{X} \right )^{2}}{n}. We do this because
The second formula is likely to underestimate the standard deviation of the population (it’s a biased estimate).
