Topic 5: Two-Sample Hypothesis Testing

Question 1

Key features of Between subject designs (3)

Answer 1

1. Each participant participates in one and only one group
2. Comparisions made between the groups
3. Random assignment used to assign participants to groups (if true experiment)

Question 2

Two group designs do not always have to…… for example …..

Answer 2

• compare an experimental group to a control
• fpr example, it can compare two different amounts of an IV (comparision of length of prision centre such as 2 years and 4 years) or compare an “apple vs orange” such as how good people do depending on AM/PM lecture

Question 3

Ex-Post-Factor (2)

Answer 3

• IV not manipulated (already occured)
• Does not allow cause and effect claims

Question 4

One sample T test vs Independent sample t-test

Answer 4

• 1 sample: you find the sample distribution and standarize it
• Independent sample: look at the difference between the sample means and compare that diff to 0. *Standaridize the difference

Question 5

How do we know if variances are equal?

Answer 5

Not equal if one variance is more than 3x the other

Question 6

Three necessary conditions to use a t-test for independent samples:

Answer 6

1. The samples must be independent
2. Each population should have a normal distribution. However, this assumption is frequently violated with little harm as long as n>25
3. Homogeneity of variance: Both groups must be sampled from populations with similar varince, if not do not pool variance, use adjusted df

Question 7

Two-Sample t-test for the difference between Means steps:

Answer 7

1. State the claim mathematically. Identify the Null and alternative hypotheses
2. Specify the level of significance (identify alpha)
3. Identify the degrees of freedom and sketch the sampling distribution (df= n1+n2 -2 or df= smaller of n1-1 or n2-1)
4. Describe the critical values (t-table)
5. Determine the rejection region(s)
6. Find the standaridized test statistic with formula below
7. Make a desicion to reject or fail to reject null
8. interpret the desicion in the context of the original clai

Question 8

Power (2)

Answer 8

• Probability of rejecting a false H0
  probability that you will find difference thats really there
• 1-beta

Question 9

Beta

Answer 9

• The probability of making a type 2 error

Question 10

1-B

Answer 10

Chance of finding an effect that exist

Question 11

Influences on power+the disadvantages of each ways (5):

Answer 11

• Increase alpha value increases the ability to find an effect: raising alpha levbel increases our probability of a type 1 error
• One tail test increase power: not appropriate for a non-directional hypothesis, goes against convention as many do 2 tail test without specifying
• Decrease population variance (σ) which is impacted by population SD and sample size: Results are harder to generalize
• Increase sample size increases power as the sampling distribution for means are skinnier: may be hard/expensive to get alot of ppl
• Make your manipulation strong aka effect size: may not be ethical

Question 12

Effect size + formula (2)

Answer 12

• Magnitude of true difference between null and alternative hypotheses (u1-u2)
• d= l (u1-u2)/σ l

Question 13

Large effect size means that

Answer 13

your null and HA population dont overlap very much

Question 14

Delta

Answer 14

Value used in referring to power tables that combines effect size and sample size

Question 15

variance and SD relationship

Answer 15

SD is the value when variance is sqaure rooted
SD^2= Variance

Question 16

Standard deviance symbol

Answer 16

σ

Question 17

Variance symbol

Answer 17

σ2

Question 18

What does this mean: Estimated power for delta= 1.5, alpha=0.05 and is roughly 0.32?

Answer 18

If the study were to run repeatedly, 32% of the time, the result would be statistically significant

Question 19

Steps to find out what sample size we need to give us the power to detect a difference (3):

Answer 19

1. Start with anticipated effect size (d)
2. Determine delta required for desired level of power
3. Calaculate n required for that value of delta

Question 20

Importance of power when evaluating study results

Answer 20

• When a result is statistically significant: Effect size can tell us whether the result is practically significant
• When a result is not statistically significant: May not be that there is no difference, but simply that the study lacked the power to find it

Question 21

Why does larger sample make distribution narrower when talking about impact of sample size on power

Answer 21

Since the standard deviation of the sampling distribution decreases with increasing n, the curve has a narrower, taller graph as more probability is squeezed toward the middle.

Question 22

Matched pair (2)

Answer 22

• When participants are measured and equated on some variable and then assigned to each group based on that
• can be experimental or quasi-experimental (non-randomization)

Question 23

Natural pairs (4)

What it is+ wjat kind of experiment+ ex+ advantage/disadvantage

Answer 23

• When participants are matched based on some biological or social relationship
• Typically quasi-experimental
• Ex: using siblings: may differ in personality but similar genectics and childhood experience.
• The primary advantage of the natural pairs design is that it uses a natural characteristic of the participants to reduce sources of error. The primary limitation of this design is often the availability of participants. The researcher must locate suitable pairs of participants (such as identical twins) and must obtain consent from both participants

Question 24

Repeated Measures

Answer 24

Where the same participants are exposed to and measured in both conditions

Question 25

Matched pair vs Natural pair

Answer 25

In a natural pairs design, scores were paired for some natural reason. In a matched pairs design, scores are paired because the experimenter decides to match them on some variable.

Question 26

Dependent (Paired) Samples design

Answer 26

- When we compare either the same participants or participants who have some type of predetermined relationship. - Subjects in one group do provide information about subjects in other groups. The groups contain either the same set of subjects or different subjects that the analysts have paired meaningfully.

Question 27

Within-subjects designs ex (3):

Answer 27

- matched pairs - Natural pairs - repeated measure

Question 28

Dependent (paired): advantages (3)

Answer 28

- Greater control over the equality of groups - more statistical power to find an effect: variability due to individual differeces decreased/nonexistent - can often have smaller sample sizes

Question 29

Which method to use if you dont have alot of people or you have alot of variability in a population?

Answer 29

Dependent (paired)

Question 30

đ

Answer 30

the mean of the diffferences between each data pair in a paired t-test

Question 31

d

Answer 31

The difference between each data pair: d= x1-x2

Question 32

Answer 32

The SD of the differences between the each data pair

Question 33

Assumptions of the Paired t-test

Answer 33

1. The samples must be dependent (paired) 2. Both populations must be normally distributed

Question 34

What are we comparing for a paired t-test?

Answer 34

We are comparing our average difference to a null hypothesis that the average difference between out two groups is 0.

Question 35

t-test for the difference between paired means steps (9)

Answer 35

1. State the claim mathematucally. Identify the null and alternative hypotheses 2. Specify the level of signifcance 3. Identify the degrees of freedom and sketch the sampling distribution [df= (number of pairs: n) -1] 4. Determine the critical values (Use t-distribution) 5. Determine the rejection regions(s) 6. Calculate d bar and Sd 7. Find the standardied test statistic of the t value with formula. 8. Make a desicion to reject or fail to reject the null hypothesis. (depends if t-observed is in the rejection region or not) 9. Interpret the desicion in the context of the original claim

Question 36

We will use t-tests exclusively for tests of ------- and the z-test for tests of -----.

Answer 36

- tests of either independent or dependent group means - proportions

Question 37

t-tests can be used for comparing means of ------ level variables

Answer 37

- interval and ratio

Question 38

statistically significant

Answer 38

Is the difference large enough that we can reject the null hypothesis of no difference?

Question 39

Z-tests can be used to compare proportions of ----- level variables.

Answer 39

nominal and ordinal

Question 40

When to use t and z test, 2 components:

Answer 40

The t-test is used when the population variance is unknown, or the sample size is small (n < 30). At the same time, the z-test is applied when the population variance (σ2) is known and the sample size is large (n > 30).

Question 41

As the number of samples and/or the size of the samples increase, the standard error becomes....

Answer 41

smaller and smaller indicating less variation around the population mean.

Question 42

The smaller the standard error, the more --- the estimate of the population mean.

Answer 42

precise

Question 43

The central limit theorem states that

Answer 43

the sampling distribution of the mean will always be normally distributed, as long as the sample size is large enough. Regardless of whether the population has a normal, Poisson, binomial, or any other distribution, the sampling distribution of the mean will be normal.

Question 44

The probability associated with a difference between two means can be determined once .....

Answer 44

the difference is standardized as a t-statistic. A calculated t-value with an associated probability in the “rejection region” in either of the two tails of the distribution would provide evidence that there is a difference between the two means.

Question 45

If we expect there will be a difference between the two means but are not predicting that one will be larger than the other, this would constitute a ---

Answer 45

two-tailed test

Question 46

As you learned previously, the t-distribution is ---- whose shapes depend on ----

Answer 46

- a family of distributions - their degrees of freedom (df)

Question 47

degrees of freedom

Answer 47

refer to the number of values in a calculated statistic that are free to vary (do not have a fixed value).

Question 48

Explain why its df-1 for degrees of freedom

Answer 48

If you are given the first three numbers in a distribution of four numbers as 2, 4, and 5, and then must identify the fourth number so that all four numbers will add to 20, the fourth number must be 9. The first three numbers can vary, but once they are determined, the last number is no longer free to vary. So we say that this distribution has n – 1 degrees of freedom, or df = 3.

Question 49

Both methods, Z and T-test assume a -------, but the z-tests are most useful when the ----

Answer 49

- normal distribution of the data - standard deviation is known.

Question 50

When do we use a pooled estimate of the standard error

Answer 50

For independent sample means, if one variance is no more than twice the other, they are considered approximately equal, and a pooled estimate of the standard error can be used.

Question 51

Answer 51

sample variances

Question 52

Using a pooled estimate when the variances are "too different" has been shown to lead to

Answer 52

unreliable results with the t-test (i.e., low p-values)

Question 53

Figuring Degrees of Freedom – Approximately Equal Variances:

Answer 53

Question 54

The p-value ---- as the df decrease

Answer 54

increases

Question 54

The variance that determine if we use a T test or Z test is the

Answer 54

variance for the population providing the samples

Question 55

How to use the p-value method approach for independent sample means

Answer 55

- calculate the p-value of t and compare that to the probability limit set by alpha - Ex: the p-value associated with a t-statistic of 10.00 and df = 48 is P < .00001. Since the P-value is less than the alpha limit of .05, the null is rejected.

Question 56

The value for d tells us

Answer 56

the mean difference between the two groups is equivalent to x.xx standard deviations