Module 8, Hypothesis Testing I

Question 1

Hypothesis Testing:

Answer 1

statistical procedure for testing whether a research hypothesis provides a plausible explanation for experimental findings

Question 2

Value of competing hypotheses

Answer 2

Two competing hypotheses are initially proposed; data is then gathered and statistical tests carried out determine which of the two hypotheses can be rejected or supported based on that data analysis
Considers the probability that the outcome of a study could have occurred in the absence of any effect of the experimental procedure or any difference between the populations being measured

Question 3

Key Elements of an Experiment

Answer 3

Research hypothesis that summarizes the outcome to be tested
Null hypothesis that is complementary to the research hypothesis and summarizes the state of affairs, if the alternative hypothesis cannot be supported
Descriptions of the variables being tested, and an explanation of control measures for extraneous variables
Description of population of interest; how population is represented in the experiment
Identification of the experimental group and control group
Statement defining how the results are to be measured and interpreted

Question 4

Null Hypothesis

Answer 4

H0: statement about a population parameter that is assumed to be true unless there is convincing evidence to the contrary, OPPOSITE OF ALTERNATIVE HYPOTHESIS
Hypothesis that our experimental group came from the population of normal responders; therefore it is representative and there was no effect, everyone might as well have been in the same group

Question 5

Alternative/research Hypothesis

Answer 5

H1: statement that is directly contradictory to the null hypothesis
Hypothesis that our experimental group did NOT come from the population of normal responders/same population as the control group

Question 6

Which hypothesis is the one being tested?

Answer 6

NULL HYPOTHESIS IS THE ONE BEING TESTED, NOT THE ALTERNATIVE: IF THE NULL HYPOTHESIS CAN BE REJECTED, THEN SUPPORT ACCRUES FOR THE ALTERNATIVE HYPOTHESIS

Question 7

Directional Hypothesis:

Answer 7

states that one measure will be more or less than a comparison measure; SPECIFIES THE DIRECTION OF THE EXPECTED DIFFERENCE
NON-DIRECTIONAL HYPOTHESIS: STATES THAT TWO MEASURES WILL BE DIFFERENT FROM EACH OTHER, BUT DOESN’T SPECIFICY THE DIRECTION OF THE DIFFERENCE (most real world research hypotheses are non-directional)

Question 8

If alternative hypothesis is directional

Answer 8

If alternative hypothesis is directional, the null hypothesis should predict that the populations are not different IN THE EXACT WAy predicted by the alternative hypothesis

Question 9

The Comparison Distribution

Answer 9

Statistical distribution to which the results of a study are to be compared
Represents the situation or the true state of affairs in the case where the null hypothesis is true

Question 10

Cutoff Score

Answer 10

Critical value that marks certain areas of the comparison distribution used as a reference for tests of significance
A z score that cuts off a given proportion of the distribution’s scores in one of the tails of the distribution acts as a marker for that area

Question 11

One Tailed:

Answer 11

an alternative hypothesis that predicts a more than outcome or a “less than” outcome, leads to a one tailed test
Since the predicted outcome is in a SPECIFIC direction, only a result in that direction can justify the rejection of the null hypothesis

Question 12

One Tailed: Right-Tailed vs. Left-Tailed Test

Answer 12

PREDICTION OF HIGHER SCORE = RIGHT TAILED TEST
PREDICTION OF LOWER SCORE = LEFT TAILED TEST

Question 13

Two-Tailed Test

Answer 13

A hypothesis that predicts a “different from” outcome and doesn’t specify a direction of the effect that leads to a two-tailed test, because an outcome in either direction can justify the rejection of the null

Question 14

Rejection Region

Answer 14

Alpha sets the significance level of the test and determines the size of the rejection region
A test statistic, z-score or t-score, that exceeds the predetermined critical value provides evidence for rejecting the null hypothesis in favour of supporting the alternative hypothesis

Question 15

Statistical vs. Practical Significance

Answer 15

Something can be statistically significant without being practically significant
Statistical Signifance: probability that the observed difference occured by chance less than 0.05; a set of measurements or observations in a study is said to be statistically significant if it is unlikely to have occurred by chance

Question 16

Effect Size:

Answer 16

way of quantifying the size of the difference between two groups so that we can better judge the practical significance of the results

Question 17

PROBLEM WITH ONLY USING P VALUES WITHOUT CONSIDERING EFFECT SIZE:

Answer 17

: SAMPLE SIZE DIRECTLY AFFECTS THE CALCULATION OF THE RESULTS
The larger the sample size = the larger the cal;culated value of the test statistic

Question 18

Cohen’s D

Answer 18

Used when comparing mean scores of two groups
D of 1: tells us that the two groups means differ by ONE STANDARD DEVIATION
Effect size of 0 would place the mean of group 2 at the 50th percentile of group 1, so the distributions overlap completely

Question 19

Type I vs. Type II Error

Answer 19

Type I Error: rejecting the null hypothesis when it is true; OUTCOME REPRESENTS A FALSE POSITIVE
TYpe II Error: say null hypothesis is true when its actually false; PROBABILITY OF A TYPE 2 ERROR INCREASES AS THE PROBABILITY OF A TYPE I ERROR DECREASES (INVERSRLY RELATED TO THE LEVEL OF SIGNFICANCE), REPRESENTED BY BETA

Question 20

Power of a test

Answer 20

Power of a test is equal to the probability of maing a correct decision and rejecting the null hypothesis when it is false (PROBABILITY OF DETECTING AN EFFECT IF THERE IS ONE)

Question 21

FACTORS IMPACTING POWER:

Answer 21

sample size (larger n=greater power), significance level, the higher the value of alpha the higher power of the test (increasing alpha has the effect of increasing the size of the rejection region and decreasing the size of the non-rejection region=greater likelihood of rejecting the null hypothesis), true value of the parameter being tested (the greater the diff between the true value of a parameter and that specific in the null hypothesis, the greater the power of the test)

Question 22

Problem with increasing alpha to increase power?

Answer 22

Increases probability of making a Type I error
because alpha is the probability of a type I error

Question 23

hy does less variability increase power

Answer 23

That is, less within-group variance will allow the treatment effect between groups in the numerator to be more apparent.

Question 24

why does a further location of true parameter increase power?

Answer 24

The location of the true mean. The further it is away to the tested one, the easier it is to detect the difference and reject the H0 , which implies a higher power of a test; Significance level α .

Question 25

What is hypothesis testing based on?

Answer 25

Based on probability theory and the Central Limit Theorum

Question 26

Why is a non-directional hypothesis the default in research?

Answer 26

If the direction you predicted the effect would be in is wrong, you’ll have to say that you didn’t find anything
Using a directional hypothesis is taking a much bigger risk

Question 27

Statement of equality in a null hypothesis, why does an alternative hypothesis not have this?

Answer 27

Null Hypothesis is written first: statement of equality, null is two groups are equal or < or equal to or > or equal to, IF H0 IS FALSE HA MUST BE TRUE
H0
Alternative hypothesis: NEVER CONTAINS A STATEMENT OF EQUALITY, we never say that groups will be equal because that’s counterproductive to the experiment itself IF HA IS FALSE, H0 MUST BE TRUE

Question 28

How are the null and alternative hypotheses complementary to one another?

Answer 28

both of these sentence cover all of the possible outcomes, lower or higher or the same from each other

Question 29

Test Statistic

Answer 29

results of a statistical test relating observed scores (usually means) to a standardized distribution

Question 30

P Value

Answer 30

probability value, what isthe probability of obtaining an observed test statistic (calcualted from the sample data) with a value this extreme if the null hypothesis is true?

Question 31

What does an alpha level of 0.05 mean?

Answer 31

a=0.10 (90 percent confidence level) 0.05 (95 percent confidence level), and 0.01 (99 percent confidence level)
We;re okay with anything LESS THAN 5% chance that the null is true: that’s why we typically use 0,05
By setting the level of significance at a small value, you are saying that you want the probability of rejecting a true null hypothesis to be small

Question 32

k

Answer 32

the population mean for the null population, the mean of the control group could be an example
EXAMPLE: ALTERNATIVE Ha: mu > k (mean score of experimental group will be higher than mean score of the control group)
NULL H0: mu < or equal to k (mean scores of both groups are the same or experimental groups score lower)

Question 33

Critical Values

Answer 33

point at which we can reject the null hypothesis, corresponds to the alpha level
Can find the value of our test statistic for which there is only a 5% likely to get a value more extreme/higher/lower/ than that: we find this value from distribution tables

Question 34

When do we reject the null hypothesis?

Answer 34

We reject the null when our calculated test statistic exceeds the critical value