statistics 2-10
Why should we think in terms of "failing to reject" the null, rather than just accepting it? (9)
"We can't reject" the null because we never directly test it. Remember, nulls reflect population characteristics, and the whole point is that we cannot directly test populations, only samples. If we can't test it, how can we reject it?
Rank the following correlation coefficients on strength of their relationship ( List the weakest first). ( 5) +.71 +.36 -.45 47 -.62
+.36 .-45 .47 .-62 +.71
Why does the standard deviation get smaller as the individuals in a group score more similarly on a test? (3)
As individuals score more similarly, they are closer to the mean, and the deviation is smaller as well.
Why is it "harder" to find a significant outcome ( all other things being equal) when the research hypothesis is being tested at the .01 rather than .05 level of significance?
At the .01 level, less room is left for errors or mistakes because the test is more rigorous. In other words, it is "harder" to find an outcome that is sufficiently removed from what you would expect by chance ( the null hypothesis) when that probability associated with that income is smaller ( such as .01) rather than larger ( Such as.05)
Why is a z score a standard score, and why can standard scores be used to compare scores from different distributions with one another? ( 8)
Because it is based on the degree of variability within it's representative distribution of scores. A z score is always a measure of the distance between the mean and some point on the x-axis ( regardless of the mean and standard deviation differences from one distribution to the next). Because the same units are used, the z-scores can be compared to one another.
For the following situations, write out in words a research hypothesis. C. Blaire is almost sure that his monthly cost for the past year are not represented of his average monthly cost over the past 20 years. (10)
Blair's cost for the month are not different from his average monthly cost over the last 20 years.
What does chance have to do with testing research hypothesis? (9)
Chance is reflected in the degree of risk ( Type I error) that we are willing to take in the possible rejection of true all hypothesis.
Describe construct validity and give an example of how each is measured. (6)
Construct Validity= is present when a testing instrument assesses an underlying construct. Example: how well does an observation tool assess one dimension of manic depression
Describe content validity. Give an example on how each is measure. (6)
Content Validity= it samples from an entire universe of possible items. Example: Does a high school history test on the American Revolution contain items that elect that subject of American History.
Why can't correlations be used as a tool to prove a cause relationship between variables, rather that just and association? ( 5)
Correlations are reflections of how much two variables have in common, but what they have in common may have nothing to do with what causes one, or the other, variable to increase or decrease.
Given the following information, would your decision be to reject or fail to reject the null hypothesis? Setting the level of significance at .05 for decision making, provided an explanation for your conclusion. ( 9) B. The null hypothesis that there is no relationship between the amount of coffee consumption and GPA (p= .62)
Fail to reject the null hypothesis. The probability is greater than .05, meaning there is no relationship between the amount of coffee consumed and GPA.
Why would you expect more variability on a measure of personality in college freshman that you would on a measure of height? (3)
For the most part, first-ayr students have stopped growing by that time, and the enormous variability that one sees in early childhood and adolescence has evened our. On a personality measure, however, those individual differences seem to be constant and are expressed similarly at any age.
What are the characteristics of the normal curve? What human behavior trait, or characteristic can you think of that is distributed normally? (8)
In a normal curve, the mean, median, and mode are equal to one another; the curve is symmetrical about the mean; and the tails are asymptotic. Height and Weight are examples, as are intelligence and problem-solving skills.
How can a test be reliable and not valid? Why is a test not valid unless it is reliable? ( 6)
In general, a test that is reliable but not valid does what it does over and over, but it does not do what it is supposed to do. And, oops! A test cannot be valid without being reliable, because if it does not do anything consistently, then it certainly cannot do one thing consistently.
What's wrong with the following statements? (9) B. It is possible to set the Type I error rate to zero
It is impossible to set the error rate to zero because it is not possible that we might not reject a null hypothesis when it is actually true. There's always a chance that we would.
What do we mean when we say that the null hypothesis acts as a starting point? (7)
It's a statement of equality. It's unbiased, and objective starting point because it is the place where everything is thought to be equal unless proven otherwise.
In general terms, describe what a test would be like if it were reliable but not valid. Now, Do the same for a test that is valid but not reliable. (6)
It's simple. A test must first be able to do what it does over and over again ( reliability) before one can conclude that it does what it should ) validity). If a test is inconsistent ( or unreliable) the it can't possibly be valid. For example, although a test consisting of items like this one 15x3=? is reliable, if the 15 item on the test were labeled "Spelling Test," the test surely would not be valid.
When two variables are correlated ( such as strength and running speed), they are associated with one another. But if they are associated with one another, then why doesn't one cause the other? (5)
Just because two things are related does not meant that one causes the other.
What's wrong with the following statements? ( 9) A. A Type I error of.05 means that 5 times out of 100 we will reject a true null hypothesis.
Level of significant refers only to a single, independent test of the null hypothesis and not to multiple test.
Given the following information, would your decision be to reject or fail to reject the null hypothesis? Setting the level of significance at .05 for decision making, provided an explanation for your conclusion. ( 9) C. The research hypothesis that a negative relationship exists between the number of hours worked and level of job satisfaction (p=.51)
Nope no relationship with a probability that high
Create a null, research, and nondirectional hypothesis for this statement. A. What are the effects of attention span on out-of-seat classroom behavior. ( 7)
Null= Children with short attention spans, as measured by the Attention Span Observation Scale, have the same frequency of out-of-seat behavior as those with long attention spans. Directional= Children with short attention spans, as measured by the Attention Span Observation Scale, have a higher frequency of out-of-seat behavior than those with long attention spans. Nondirectional=Children with short attention spans, as measured by the Attention Span Observation Scale, differ in frequency of out-of-seat behavior than those with long attention spans.
Describe predictive validity and give an example of how each is measured. (6)
Predictive validity= examines how well a test predicts a particular outcome. Example: how will does a test of spatial skills predict success as a mechanical engineer?
Given the following information, would your decision be to reject or fail to reject the null hypothesis? Setting the level of significance at .05 for decision making, provided an explanation for your conclusion. ( 9) A. The null hypothesis that there is no relationship between the type of music a person listens to and his propensity for crime ( p< .05)
Reject the null hypothesis. Because the level of significance is less than 5%, there is a relationship between a person's choice of music and his or her crime rate.
Why is significance an important construct in the study and use of inferential statistics? (9)
Significance sets the criterion for being confident that the outcomes we observe are "truthful." It further determines to what extent these outcomes can be generalized to the larger population from which the sample was selected.
Provide an example of when you would want to establish test-retest and parallel forms on reliability. ( 6)
Test-retest reliability should be established when you are insterested in the consistency of an assessment over time, such as pre and posttest studies or longitudinal studies. Parallel forms reliability is important to establish to makes sure those different forms of the same test are similar to one another.
What's with the z in Z-test? What similarity does it have to a simple z or standard score? (10)
The (BIG) Z is a similar to the small z for one very good reason: It is a standard score. The z score has the sample standard deviation as the denominator, whereas the z-test value has the standard error of the mean ( or a measure of the variability of all the means from the population) as the dominator. In other word, they both use a standard measure that allow us to use the normal curve table.
The mean of a set of test scores is 50, and the standard deviation is 5. For a raw score of 55, the corresponding z scores is +1. What's the z score when the standard deviation is half as much, or 2.5? From this examples, what can you conclude the effect of decreasing the amount of variability in a set of scores is on a standard score( given all else is equal, such as the same raw score) and why is this effect important? ( 8)
The amount of variability in the set of scores is half as much, and the corresponding z score is twice as larger ( it went from 1 to 2). This indicates that as variability increases, and all other things are help constant, the same raw score becomes more extreme. The less the difference between scores ( and the lower the variability), the less extreme the same score will be.
What is statical significance? (9)
The idea that certain outcomes are due, not to chance, but to factors that have been identified and tested by the researcher. These outcomes can be assigned a value to represent the probability that they are due to chance or some other factor or set of factors. The statistical significance of these outcomes is the value to that probability.
What's wrong with the following statements? (9) C. The smaller the Type I error rate, the better the results.
The level of risk that you are willing to take to reject the null hypothesis when it is true has nothing to do with the meaningfulness of the outcomes of your research. You can have a highly significant outcome that is meaningless, or you can have a relatively high Type I error rate (.10) and a very meaningful findings.
What does the (idea of the) critical value represent? ( 9)
The minimum value at which the null hypothesis is no longer the accepted explanation for any differences that are observed. It is the cut point: Obtained values that are more extreme indicate that there is no equality but a difference ( and the nature of that difference depends on the questions being asked). Do Remember that this cut point is set by the researcher ( even if .01 and .05 are conventional and often used cut pointe).
Why the null in bel hypothesis? (7)
The null( which literately means "void") represents the lack of any observed differences between groups of outcomes. There's nothing there, which is the state of affairs that we have to begin with given no information.
When is it appropriate to use the one-sample z-test? (10)
The one-sample z-test is used when you want to compare a sample mean to a population parameter. Actually, think of it as a test to see whether one number( which is a mean) belongs to a huge set of numbers.
Why is the range the most convenient measure of dispersion, yet the most imprecise measure or variability? When would you use the range? (3)
The range is the most convenient measure of dispersion, because it requires only that you subtract on number ( the lowest value) from another number ( the highest value). It's imprecise because it does not take into account the values that fall between the highest and the lowest values in a distribution. Use the range when you want a very gross ( not precise) estimate of the variability in a distribution.
For the following situations, write out in words a research hypothesis. B. The health department is charged with finding out whether the rate of flu per season is comparable to the average rate during the past 50 seasons. (10)
The rate of flu infections per 1,000 citizens for the past flu season is not comparable to the rate of infection over the past 50 seasons.
To compute a standard score, what three bits of information of you need? ( 8)
The raw core, the mean, and standard deviation.
For the following situations, write out in words a research hypothesis. A. Bob wants to know whether the weight loss for his group on the chocolate-only diet is representative of weight loss in a large population of middle-aged men. (10)
The weight loss of Bob's group on the chocolate-only diet is not representative of weight loss in a large population of middle-aged men who are on a chocolate- only diet.
Standard scores, such as z scores, allow us to make comparisons across different samples Why? (8)
They use the same metrics-standard deviation- and we can compare scores in units of standard deviations.
A major research study investigated how representative a treatment group's decrease in symptoms was for a certain drug when the sample was compared to the entire population. It turn's out that the test of the research hypotheses resulted in a Z-test score of 1.67. What conclusion might the researcher put forth? Hint: Notice that the Type I error rate or significance level is not stated ( as perhaps it should be). What do you make of all of this? (10)
What's missing here is the significance level at which the hypothesis is being tested. If the level .01, then the critical z value for rejecting the null and concluding that the sample is different from the population is 1.96. If the level at which the hypothesis is being tested is .05, then the critical z value is 1.65. Seems this presents the most interesting of questions regarding the trade-off between making a Type I error ( 1% or 5% of true nulls being rejected) verses stating statical significance.
Why do good samples make for good tests of research hypothesis? What is the danger in not selecting a representative sample. ( 7)
When you have a good sample, you can get a more true reading of actual population characteristics, and everything from your most basic findings to your inference to other populations is increased in accuracy. Poor sample selection= crummy population representation.
When testing any experimental hypothesis, why is it important that the test you use to measure the outcome be both reliable and valid? (6)
You need to use both a reliable and a valid test because if you get a null result, you will never be sure whether the instrument is not measuring what it is supposed of the null hypothesis is actually faulty.
Under what conditions would you use the median rather than the mean as a measure of central tendency? Why? Provide an example of two situations in which the median might be more useful that the mean as a measure of central tendency.(2)
You use the median when you have extreme scores, which would disproportionately bias the mean. One situation in which the median is preferable to the mean is when income is reported. Because it varies so much, you want a measure of central tendency that is insensitive to extreme score or an outlier, such as the speed with which adolescents can run .
Suppose you are working with a data set that has some very "different"( much larger or much smaller that the rest data) scores. What measure of central tendency would you use and why? (2)
You would use the median because it is insensitive to extreme scores.
