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- StudyBlue
- Wisconsin
- University of Wisconsin - Madison
- Psychology
- Psychology 210
- Hendricks
- Though Questions Unit 2

Robyn A.

1.
What is the
difference between a population, sample, and sampl__ING__ distribution (think
about conceptual differences – what they are composed of and what they are used
for – and the symbols that are used for each)?

- Population - uses greek letters - entirety of what your studying-variability=sigma, center is μ
- Sample - subset of population, usually representative of the population - english letters-center = M, varib =s
- sampling distribution - distribution of sample means, variab=σ
_{M}. mean=μ, infer from samples about population

2.
What is the
difference between an empirically derived and a population derived
(theoretical) sampling distribution?
What are advantages and disadvantages of each?

- Empirically derived is trial and error. take repeated samples of a population and find all the means. then find the mean of those means. --CON-time consuming
- Population derived - based on CLT1 -CON- need to know population

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3.
What does the
Central Limit Theorem (CLT) suggest regarding the characteristics of the
sampling distribution of the mean?

normalcy increases as n increases

variabilty = σ
4.
What impact
does sample size have on our sampling distributions? As we increase our sample size, what happens
to sampling error? What is the standard
deviation of a sampling distribution called?

- the bigger the sample size the more clustered around the, the narrower it is.
- sampling error decreases
- σ
_{M}

5.
Earlier we
described the sample M as an unbiased estimator of μ. How is that fact
illustrated by, or related to, the CLT?

the sampling distribution is centered around and has a mean is μ

6.
What is the
relationship between the shape of the population and the shape of the sampling
distribution? Why is this important?

There isn't one. they are independent of each other

7.
Be able to
give some practical applications of the sampling distribution. How might it be of practical use? To what kind of situations does it apply?

- mean age of jurors
- battery life
- any problem relating M's

8.
Be able to explain how the CLT permits
us to estimate the position of m if we only know
sample information? Be able to explain
my “reverse logic” for this estimation.
Why is it that we can take info from __one__ sample and infer things
about the population?

- only 5/100 times the μ will not fall with the intervals set by the means
- can infer things about population through the samples
- without the CLT we can not predict/set probability

9.
What is the difference between the scientific
and statistical hypotheses? Explain what
is represented by the null and alternate hypotheses? Be able to generate examples of each. Specify attributes of each. Why do we focus so much on the null
hypothesis for hypothesis testing?

- Scien:what you want to find --alt hypoth
- Stat: what you want to disprove -null hypoth
- focus on null because easier to prove some thing wrong once than prove it right for every possible case

10.
Explain the difference between directional
and non-directional hypotheses. What are
the implications of using a one-tail vs. two-tail hypothesis test? When should each be used?

- directional-one tailed-shows an increase or decrease in the treatment--better power
- non directional--two tailed--more conservative and safer--when in doubt use this --shows a change(significance)but not which direction

11.
What is meant by a Type I error (be
sure that you can describe it in practical terms, for a real investigation, not
just referring to the null hypothesis)?

- reject null when you shouldn't have
- claim significance when there is none
- purely happens by chance--experimenter has no control over it
- represented by alpha

12.
If α = .05, what does that mean (in
practical terms)? Why don’t we set alpha
even lower?

- the lower alpha, the higher beta, the lower power. = bad
- there is a 5% chance of committing a type 1 error
- means found in that region are considered significant and not due to chance

13.
Why do scientists want to minimize Type
I errors? Think about potential costs
associated with a Type I error?

- can create false hope for patients
- money
- integrity
- reputation for science and scientist
- time--delays
- may not consider treatments that actually work

1.
What is meant by a Type II error (again
think in practical terms)? What are some
factors that influence the likelihood of this error?

- claim no significance when there actually was significance
- represented by beta
- fail to reject the null
- Factors:
- ---sample size
- ---diff to be detected
- ---variabilty
- ---test type (directional? dependent?)

15.
Explain the way(s) in which the
experimenter influences or has control over Type I and Type II errors (direct
& indirect).

type 1-experimenter sets alpha level

type 2--sample size choice, directionality chosen, dependence chosen

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16.
What is the difference between Type I
and Type II errors vs. biases (malfeasance) in the conduct of research?

- type 1 happens purely buy chance, the experimenter has no control and did nothing wrong
- type 2- experimenter choses sample size and the other factors listed previously and therefore has more blame in committing of a type 2 error

17.
Explain the connection between sampling
distributions (the CLT) and hypothesis testing.

without the CLT hypothesis testing would not be possible the sampling distribution is made and set around the mean which is used in the null and alternate hypothesis of hypothesis testing

18.
What is meant by “statistical
significance”? What is meant by “p <
.05”? This is a probability of
what? Under what circumstances do we
make such statements?

the event is not due to chance, what happened took plae because of the treatment or testing done. there is <5% chance of committing a type 1 error

tobs>tcrit

19.
What is a confidence interval, and what
does it reveal? What is it centered
around? How is it related to hypothesis
testing? How is it different?

· Says that 95% of the sample means will fall within a given confidence int.—the μ will fall w/in this as well

· Both hypoth and conf int based on alpha level—foundation material is similar

· Hypoth testing based on null hypoth, conf int based on actual outsomes (range)

· Suggested as an alt to hypoth testing

· Follow up to 2 tailed
20.
What is the difference between a point
estimate and an interval estimate?
Discuss their usefulness.

·
Point estimate is a mean

· Interval estimate is confidence int

21.
Be able to describe Cohen’s effect
size. What is meant, in practical terms,
for a small, medium, or large effect size?

· In std dev units

· Shows how much a treatment actually effected a condition

· Measure of magnitude
22.
What does an effect size contribute
that significance does not? Is it
possible to derive significance, but have a weak effect size? When might this be more likely?

· Significance only tells if something had an effect or not, effect size tells you how much of an effect it actually had

· Easier to have significance but small effect size with large n
23.
What is meant by power? Why is it important? Be sure to understand our power diagram.

· Ability to detect a change in the data if such a change actually occurred

· Power = 1 – β

· Can see if a treatment will be effective before testing is actually done

· Power increases as type 2 error decreases
24.
Why must a specific alternative
hypothesis be identified to calculate power?
How does this hypothesis differ from our original hypotheses?

·
Tells you what change you are looking
for you, if you do not specify a specifc hypoth you could be looking at a
infinite # curves

25.
Be able to demonstrate the impact of
several variables (e.g., a, n, directional/non-directional tests,
discrepancy to be detected, variability) on power and b. Think about what each does to our power
diagram.

· Sample size increase power increase—width shrinks

· Direction -> non directional—alpha decreases, beta increases, power decreases

· Discrepancy to be detected- position of alt curve changes—difficult small differences

· Alpha changes- decreases, beta increases, power decreases—goal line changes

· Variability – position shifts, variability increases, power decreases26. What are some criticisms of, or concerns regarding, traditional hypothesis testing?

· Arbitrary significance—not based on actual consequences of type 1 error

·
__Dichotomous logic--black and white!__

· Overemphasis on significance

· Inadequate attention to other factors that influence significance- i.e. sample size, variance(poor control)
27.
What alternatives to traditional
hypothesis testing are available? How do
they differ (assumptions, interpretation, etc.)?

·
Confidence interval—*alpha level still arbitrary*

·
Alpha level based on risk –*what constitutes risk?*

28.
How does the sampling distribution of
the mean change when sigma is unknown?

·
When sigma unknown use s. there is more
variability and with s therefore curve widens, and t tests are used

29.
What is the difference between the t
and z distributions? Explain why the t
distribution needs to be wider than that for z?

z is normal.

t approaches normal with increases sample size

t has more variability and is therefore wider

with small n, s is unreliable

30.
How is the shape of the t distribution
affected by df? Explain why.

as df increases t widens

31.
We calculated the “proportion of
variance accounted for” by the IV. What
does this mean? What does it reveal
about our experiment that isn’t revealed by significance testing?

- what percentage of the total variance is accounted for by the treatment/study
- measure of magnitude in percent
- how much influence th IV had on the DV

32.
There are multiple ways of evaluating
the outcome from an investigation.
Compare the interpretation of significance, confidence interval, effect
size, power, and proportion of variance accounted for.

· Confidence int:---The actual data found, 95% of the sample means should fall within this interval—still based on alpha (CLT)—not dichotomous like hypoth testing

· Hypoth. Testing focuses on the null (what didn’t happen)

o -black and white-no gray.

· Effect size---how many std dev did the treatment chance the control

· Proportion of variance tells how much of the total variance can be accounted for by the study done
33.
How does our sampling distribution
change when we use two groups in hypothesis testing? Think about a revised CLT (call it CLT2), describing
key characteristics of this sampling distribution.

- the center is around mean
_{1}-mean_{2}, which is 0. the variability is_{sm1-m2. }-normal distribution(approaching even more normal with increasing n - made of differences between means
- very robust

34.
What is meant by independent groups designs
(a.k.a., between subjects designs or between groups designs)? Give examples.

not matched or used repeated measures

not family, social pairs, pre/post test, ect

35.
Sometimes we have equal n in two groups
that are being compared and sometimes not.
What impact does this have on our calculations? What is meant by a “pooled standard error”, and
why is that necessary?

- when equal n errors can just be averaged together, when unequal they are weighted the one wit the bigger n as more weight than the the other

·
Homogeneity of variance-if the n’s are
not close enough it is not safe to continue with the tests

36.
What is meant by homogeneity of
variance (homoscedasticity)? How can we
test to see whether our data meets this assumption? How rigid (or lenient) is the F-max test in
evaluating this assumption, e.g., do the variances have to be exactly the
same? How does SPSS evaluate this
assumption?

fmax and levine(SPSS)

fmax is very robust in that is allows much deviation from the rules

s's are close enough to continue

37.
What assumptions are behind independent
groups tests? What is meant if we say
that a given test is robust? How does
this relate to the assumptions for the independent groups test?

robust regaring normality of curve

roughly equal n's

38.
What is meant by dependent groups? Give examples of research designs
appropriately analyzed with these techniques.

paired, matched, repeated measures

39.
How is the sampling distribution
altered for dependent groups vs. independent groups (perhaps CLT3)? Compare the size of the standard error that
one would typically obtain for dependent vs. independent groups.

everything remains the same except sampling error which decreases because the consistent ind diff are accounted for and subtracted out

40.
I suggested two different ways of
calculating the standard error for dependent groups. Explain how both procedures account for
consistent individual differences in the data?

· Correlation equation subtracts out consistent indiv differenced right away

· S
41.
How does the correlation between sets
of scores influence the outcome for dependent groups? What does this suggest regarding the use of
matching variables?

· It is multiplies by the error that gets subtracted out therefore the better the correlation the lower the error.

· The better groups are matched the better the correlation the lower the error
42.
How is power affected by using
independent vs. dependent groups?
Discuss the impact of the correlation on power.

· Power is greater for dependent because there is less error

· Based on degrees of correlation- r increases power increases
43.
Consider the pros and cons for using
dependent groups for hypothesis testing.

· PROS – better power, more correlation, less error, subtract out individual differences

· CONS – difficulties in matching, carryover effects, loss of extremes
44.
What difficulties are encountered in
estimating the required sample size for a given study? What kinds of information are required before
you can estimate the appropriate sample size?

·
Need a lot of information prior to
study –need alpha, beta (power if possible) variability in data, type of test,
1/2 sample directional? In/dependent, difference to be detected

45.
How does specifying a desired effect
size help in estimating sample size? How
is this considered a short cut, i.e., what information is no longer required by
using the effect size?

· Don’t need to know variability or difference to be detectedàneed to know to know power, so good that we don’t have to know them

· Estimate ratio of cohens d—what effect size do you want? * The material on this site is created by StudyBlue users. StudyBlue is not affiliated with, sponsored by or endorsed by the academic institution or instructor.

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