Module 8

Question 1

What does a single sample t-test evaluate?

Answer 1

• whether the mean of your sample is different from some reference value

Question 2

What does a paired sample t test evaluate?

Answer 2

whether the difference in paired data is different from some reference value

Question 3

What does a two sample t test evaluate?

Answer 3

whether the means of two groups are different from each other

Question 4

What are the four steps for conducting a single sample t test?

Answer 4

• define the null and alternative hypothesis
• establish the null distribution
• conduct the statistical test
• draw scientific conclusions

Question 5

What are the null and alternative distributions for a single sample t test?

Answer 5

are statements about how your sample mean related to the reference value

m=sample mean
u=reference value

if no directionality:
m=a (Ho)
m does not equal u (Ha)

if there is directionality
m>/=u or m</=u (Ho)
m>u or m<a (Ha)

Question 6

How do you establish the null distribution for a single sample t test?

Answer 6

sampling from a statistical population that had a mean given by the reference (u) value, is a t distribution

Question 7

How do you create a statistical test for a single sample t test?

Answer 7

• done by comparing the Type I error (a) against the p value (p)

If the p-value is less that the Type I error rate (p<⍺), then we reject the null hypothesis.
If the p-value is greater than or equal to the Type I error rate (p≥⍺), then we fail to reject the null hypothesis.

Question 8

How do you draw scientific conclusions for a single sample t test? What should it include.

Answer 8

Should include
* the sample mean and standard deviation
* the observed t score (two decimal places)
* degrees of freedom
* p value (three decimal places)

Question 9

What are paired sample t tests designed to look at?

Answer 9

how sampling units change accross a factor. to accomplish this, two measurements are taken from each sampling unit; they may be taken at two points in time, or taken from two locations

THE TWO MEASUREMENTS COME FROM THE SAME SAMPLING UNIT

Question 10

What are the four steps to conducting a paired sample t test?

Answer 10

• define the null and alternative hypothesis
• establish the null distribution
• conduct the statistical test
• draw scientific conclusions

Question 11

What are the null and alternative hypothesis’ for a paired sample t test?

Answer 11

• statements about how the difference between the paired measurements is related to the reference value
• difference between the measurements: d
• reference value: u
• difference is calculated: d=x2-x1
• x2: measurement including the factor of interest
• x1=the measurement without the factor

Question 12

Null and alternative hypothesis for paired sample t test if no directionality?

Answer 12

H0: d=μ

HA: d≠μ

Question 13

Null and alternative hypothesis for paired sample t test if there is directionality?

Answer 13

H0: d≤μ (or d≥μ)

HA: d>μ (or d<μ)

Question 14

How do you establish the null distribution for a paired sample t test?

Answer 14

sampling from a statistical population where the true difference between the paired measurements was given by the reference value (u). a t-distribution

Question 15

How do you find the degrees of freedom for a paired sample t test?

Answer 15

df=n-1

n=the number of differences/sampling units

Question 16

What is the relationship between the p value and type 1 error rate?

Answer 16

If the p-value is less that the Type I error rate (p<⍺), then we reject the null hypothesis.

If the p-value is greater than or equal to the Type I error rate (p≥⍺), then we fail to reject the null hypothesis.

Question 17

How do you report a scientific conclusion for a paired sample t test?

Answer 17

• the mean difference between the paired measurements, and the standard deviation of the differences
• the observed t score (two decimal places)
• degrees of freedom
• p-value (three decimal places)

Question 18

What does it mean if we reject the null hypothesis for a paired sample t test?

Answer 18

the sample data provide strong evidence that the difference between the paired measurements is different from the reference value

Question 19

What does it mean if we fail to reject the null hypothesis?

Answer 19

the sample data do not provide strong evidence that the difference between the paired measurements is different from the reference value

Question 20

What is the distinguishing characteristic of a two sample t test?

Answer 20

the sampling units in one group are independent from the sampling units in the other groups (this is why this test is also called the independent sample t test)

Question 21

What are the four steps when conducting a two sample t test?

Answer 21

• define the null and alternative hypothesis
• establish the null distribution
• conduct the statistical test
• draw scientific conclusions

Question 22

What is the null and alternative hypothesis for a two sample t test if there is no directionality?

Answer 22

m1= the sample mean of the first group
m2=the sample mean of the second group

H0: m1=m2

HA: m1≠m2

Question 23

What is the null and alternative hypothesis for a two sample t test if there is directionality?

Answer 23

m1= the sample mean of the first group
m2=the sample mean of the second group

H0: m1≤m2 (or m1≥m2)

HA: m1>m2 (or m1<m2)

Question 24

How do you establish the null distribution for a two sample t test?

Answer 24

the null distribution for a two sample t test is the distribution of differences between the group means that you would get from sampling a statistical population where the null hypothesis was true

since the null hypothesis is that the group means are equal, the corresponding statistical population is one where you still sample from two groups, but each group has the same sample mean

Question 25

How do you conduct the statistical test for a two sample t-distribution?

Answer 25

done by comparing the Type I error rate (a) against the p-value

Question 26

What do you need to include in the scientific conclusion for a two sample t-test?

Answer 26

• the mean, standard deviation, and sample size for each group
• the observed t score (two decimal places)
• degrees of freedom
• p-valie (three decimal places