Topic 3 : Introduction to hypothesis testing

Question 1

In hypothesis testing, sample statistics are

Answer 1

used to assess the probability that the hypothesis in fact represents the true state of affairs

Question 2

What is hypothesis testing (2)?

What it is+ based on

Answer 2

• A statistical procedure: uses sample data to evaluate a hypothesis about a population
• based on probability theory and CLT

Question 3

The focal hypothesis is the

Answer 3

null hypothesis

Question 4

The Null hypothesis

What it is+population

Answer 4

• A statement about a population parameter that is assumed to be true unless there is evidence to the contary
• The hypothesis that our participants of interest came from the population of normal responders (Or the same population as the control group)

Question 5

The alternative hypothesis

What it is+population

Answer 5

• Summarizes the expected or perdicted outcome of the investigation
• The hypothesis that our participants of interest did not come from the population of normal responders

Question 6

We are testing —- and if we reject that, that means we have support for —–

Answer 6

• Hnull
• Ha

Question 7

Directional hypothesis +ex (2)

What it is + test type+ ex

Answer 7

• states that one measure (e.g. the mean of experimental group) will be more than or less than a comparison measure (e.g mean of control group)
• 1 tail test
• Ex: Ha: We think that the experimental group will score higher than the score in control group

Question 8

A non-directional hypothesis + ex (2)

Answer 8

• States that two measures will be different from eachother but does not specify the direction of the difference
• Ex: Experimental group could have scored higher or lower than control group

Question 9

Null hypothesis contains a statement of

Answer 9

equality

less than or equal, more and equal, equal

Question 10

Alternative hypothesis contains a statement of

Answer 10

inequality

Such as less than, more than, DNE

Question 11

Test statistic+ ex

Answer 11

• The results of a statistical test relating observed scores (generally means) to a standardized distribution
• Z, t

Question 12

P- value + ex (2)

Answer 12

• The probability of obtaining an observed test statistic (calculated from the sample data) with a value that extreme if the null hypothesis is true
• Ex: The people in your group become less depressed on their own, not because of your treatment” How likley is that = p value

Question 13

A very small p-value means that such an extreme observed outcome would be very —- under the null hypothesis.

Answer 13

unlikely

Question 14

Level of significance (4)

maximium+ probability+ denoted by+ ex

Answer 14

• Your maximium allowable probability of rejecting the null if it is true
• The probability of saying that the null is false when it is true
• denoted by alpha
• ex: a= 0.05

Question 15

By setting the level of significance as a small value, you are saying that you (3)

criteria+ smaller signif indicates…+ lower

Answer 15

• are making a stricter criterion for rejecting the null hypothesis. This means you’re less likely to reject the null hypothesis unless there’s strong evidence against it.
• Typically, a smaller level of significance (like 0.01 or 0.001) indicates a higher confidence requirement to reject the null hypothesis, leading to a lower chance of making a Type I error (false positive).

Question 16

critical value

Answer 16

The point at which we decide to reject the null hypothesis

Question 17

Curve in the test statistic and critical value graph

Answer 17

the null population

Question 18

Curve in the test statistic and critical value graph and the relatinship between our data

Answer 18

We want to see how unlikely our data of interest (experimental group) is part of this null population

Question 19

Statistical significance

Answer 19

likelihood that the difference between two or more variables is caused by something other than chance

Question 20

We use a left tail test when (2)

Ha

Answer 20

• we think the experimental group is lower than whatever we are comparing it too
• HA<

Question 21

We use a right tail test when

Ha

Answer 21

Our sample comes from a population where the true mean of that population is greater than the null pop mean
- The alternative hypothesis Ha contains the greater than symbol (>)

Question 22

We use a two tail test when

Answer 22

The alternative hypothesis Ha contains the not equal symbol

Question 23

We always want to frame our desicion in terms of the

Answer 23

null hypothesis

Question 24

Making desicion with Z-scores

Answer 24

compare Z-observed to Z-critical

Question 25

For a left-tailed test, if z-observed is —- than z-critical, then reject H0

Answer 25

smaller

Question 26

For a right-tailed test, if z-observed is —- than z-critical, then reject H0

Answer 26

larger

Question 27

For a two-tailed test, if z-observed is —- than z-critical, then reject H0

Answer 27

more extreme

Question 28

For a left-tailed test, if z-observed is —- than z-critical, then fail to reject H0

Answer 28

larger

Question 29

Steps for hypothesis testing (5)

Answer 29

1. Identify the null and alternative hypothesis
2. Specify the level of significance (alpha)
3. Find critical value associated with that level of signifcance and shade in rejection regions
4. calculate the observed test statistic based on collected data
5. Is the observed test statistic in the rejection region?

Question 30

Type 1 error

Answer 30

Occurs if the null hypothesis is rejected when its true (no affect but you say there is)

Question 31

Type 2 error

Answer 31

Occurs if the bull hypothesis is not rejected when it is false (You dont find evidence of an effect but there actually is)

Question 32

Probability of type 1 error denoted by

Answer 32

alpha

Question 33

Type 2 error is denoted by

Answer 33

beta

Question 34

Power (2)

Answer 34

Probability of correctly rejecting false null hypothesis
Detecting an effect thats there

Question 35

Using small alpha values reduce our chance of making a

Answer 35

type 1 error

Question 36

Power of a test + formula

Answer 36

The probability of making a correct desicion and rejecting the null hypothesis when it is in fact false
1-B

Question 37

Ways to increase power

Answer 37

• the larger the sample size, the greater power of the test
• The higher level of signifcance (alpha) the higher power(increase the size of the rejection region)
• The higher the effect size

Question 38

Higher values of the t-score indicate that ——. The smaller the t-value, ——-.

Answer 38

a large difference exists between the two sample sets
the more similarity exists between the two sample sets