Module 9, Hypothesis Testing II

Question 1

To test a hypothesis about the mean if SD is known

Answer 1

If standard deviation is known: YES, THE POPULATION IS NORMALLY DISTRIBUTED—USE Z-TEST ON ANY SAMPLE SIZE

Question 2

To test a hypothesis about the mean if SD is NOT known

Answer 2

If standard Deviation is NOT KNOWN: if there is sample size greater than or equal to 30, CAN STILL USE Z TEST

Question 3

To test hypothesis about mean If standard deviation is NOT KNOWN, sample size n<30,

Answer 3

MUST USE T TEST

Question 4

How is the t-distirbution most fundamentally different from the standard normal distribution?

Answer 4

T distribution is an entire family of distributions, unlike the standard normal distribution, which is a single distribution
Each t-distribution is determined by degrees of freedom, WHICH IS DETERMINED BY SAMPLE SIZE n

Question 5

Moderator vs mediation hypothesis

Answer 5

A mediating variable (or mediator) explains the process through which two variables are related, while a moderating variable (or moderator) affects the strength and direction of that relationship.

mediator as a go-between for two variables. For example, sleep quality (an independent variable) can affect academic achievement (a dependent variable) through the mediator of alertness. In a mediation relationship, you can draw an arrow from an independent variable to a mediator and then from the mediator to the dependent variable.

a moderator is something that acts upon the relationship between two variables and changes its direction or strength. For example, mental health status may moderate the relationship between sleep quality and academic achievement: the relationship might be stronger for people without diagnosed mental health conditions than for people with them.

In a moderation relationship, you can draw an arrow from the moderator to the relationship between an independent and dependent variable.

Question 6

Qualification for a mediating variable

Answer 6

If something is a mediator:

It’s caused by the independent variable.
It influences the dependent variable
When it’s taken into account, the statistical correlation between the independent and dependent variables is higher than when it isn’t considered.

Question 7

qualification for a moderating variable

Answer 7

Moderators usually help you judge the external validity of your study by identifying the limitations of when the relationship between variables holds. For example, while social media use can predict levels of loneliness, this relationship may be stronger for adolescents than for older adults. Age is a moderator here.

Question 8

What terms is the conclusion framed in?

Answer 8

ALWAYS want to frame our conclusion in terms of the null hypothesis: we fail to reject the null, or we reject the null (do NOT state in terms of alternative hypothesis)

Question 9

How does the percentage split work with left tailed vs. right tailed vs. two tailed tests?

Answer 9

Alpha (criticla region): area to the left of the test statistic
ALL OF THAT CHANCE/ALPHA IS IN THE LEFT TAIL
Alpha (critical region) is to the right of the test statistic
ALL OF THAT CHANCE / ALPHA IS IN THE RIGHT TAIL
A 0.05 alpha is now SPLIT between the two tails
We do NOT want 5% in each tail, so we don’t actually want to increase alpha: we still want to maintain the 5% overall

Question 10

When can we reject H0 on a left-tailed test?

Answer 10

LEFT TAILED TEST: if z-observed (what we’re calculating) is SMALLER than z-critical (one we get from the table) we can reject H0 (if z-observed is larger than z-critical, then fail to reject H0)

Question 11

When can we reject H0 on a right tailed test?

Answer 11

RIGHT-TAILED Test: if z-observed is larger than z-critical, we can reject H0 (if z-observed is smaller than z-critical, then fail to reject H0)

Question 12

When can we reject H0 on a two-tailed test?

Answer 12

TWO-TAILED TEST: if z-observed is MORE EXTREME than z-criticals, then reject H0 (if z-observed is less extreme than z-criticals, then fail to reject H0)

Question 13

How to find corresponding z critical for a one vs. two tailed test?

Answer 13

TWO TAILED: need half the alpha on the z table because its split
ONE TAILED: need the whole thing on the z table

Question 14

Alpha

Answer 14

chance of making Type I Error in relation to H0 is true (saying there is an effect when there ISN’T, false positive)
Chance of making correct decision: 1—alpha (95% of the time we’re going to get a sample that isn’t in the rejection region)

Question 15

Beta

Answer 15

chance of making Type II error (if we don’t reject H0, we say there is no effect BUT THERE IS = you don’t find evidence of an effect but it is there)
Chance of making correct decision in regards to H0 false (1–Beta)

Question 16

What is the problem with a Type II error?

Answer 16

Problem with Type II: there might be an effect, but if you didn’t have enough people then you wouldn’t detect it, or there was too much variability in the sample

Question 17

Power and reporting p-values

Answer 17

Opposite of probability of making a TYpe II error
In research we typically err on the side of making a TYpe II error rather than claiming an effect that doesn’t exist: thats why we use very small alpha values
Want to report exact P value, because it is the probability that you made a TYpe I error: how far the sample mean is from the mean of the null distribution

Question 18

Power of a Test

Answer 18

Power= 1–probability of failing to detect an effect that exists
Equal to the probability of making a correct decision and rejecting the null hypothesis when it is false
Equal to the probability of NOT making a Type II error (1—B)

Question 19

How to increase effect size?

Answer 19

Increase the size of the effect: make it so the thing you’re trying to find is more obvious, make the effect big so that it is easier to find (GREATER EFFECT SIZE (or the difference between true value of the parameter and that specified in the null) THE GREATER THE POWER OF THE TEST)
Increase the severity of the measure (show multiple severely violent videos), increase dosage of the drug or increase therapy, MORE IS MORE
^^Must keep the wellbeing of participants in mind, more is more but has to actually be within reason, this may also decrease external validity and the ability to use it outside the lab (who is watching 10 hours of violence, is it actually practically significant/ecologically valid

Question 20

to compare an individual score to a known population mean

Answer 20

use z test

Question 21

Using t table vs. z table rule

Answer 21

If we dont know population SD, we always want to use T table so we don’t underestimate, T is more conservative; if we know population distribution, because the T table is more conservative it reduces size of rejection region: IF YOU KNOW POPULATION SD THEN USE Z