CI & Two Sample t-tests

Question 1

95% CI is the same one you would look up if?

Answer 1

you were doing a two-tailed test where a = .05

Question 2

99% CI is the same one you would look up if?

Answer 2

two-tailed test where a = .01 (1%)

Question 3

What is a template for us to report the CI?

Answer 3

We can be 95% confident that the interval spanning xxx to xxx contains the true mean difference in the population

We don’ say we are 95% confident that the population mean is within this range, because mu is always unknown.

Question 4

What is one thing that sometimes get ignored when calculating CI?

Answer 4

S-x bar should be standard deviation over square root of N! Don’t forget this and just plug in the standard deviation

Question 5

What is one rule used in PSYC218 class for the df table?

Answer 5

Be conservative and round down

Question 6

What is the trick when you see that the CI does not contain the mean of the null hypothesis population?

Answer 6

Reject the null hypothesis and the result is statistically significant
If zero is contained in the CI, the result is not statistically significant

Question 7

When do we use a two samples t test?

Answer 7

When we don’t know both the mu and the sigma.

It is really common in the field of psychology.

Question 8

What are two types of two samples t test?

Answer 8

Paired samples t-test
Independent samples t-test

Question 9

When do we use the paired samples t-test?

Answer 9

• When the data from the same subject tested twice under different conditions (within subjects or repeated measures design)

Why not the sign test? The sign test only uses the direction of the changes, and completely ignores the magnitude of the changes.

Question 10

Why is the paired sample t-test stronger than the sign test?

Answer 10

Because it uses the magnitude of the changes in addition to the direction.

With the low power of the sign test, there is a high chance of making a Type II error (retaining H0 when it is false). The t test is usually more powerful than the sign test. The additional power gives H0 a better chance to be rejected if it is false.

Question 11

When do we use independent samples t-test?

Answer 11

When data comes from two independent groups (between-subjects design)

experimental group vs. control groups

Question 12

Which two samples t-test is stronger?

Answer 12

The paired-sample design is generally more powerful because each participant serves as his or her own control, one source of noise (variability) is reduced.

However, independent samples design is often more practical. Often, the same participant cannot be used twice, e.g., not testing the teen twice on TSST

Question 13

What are the two assumptions should be met in order to conduct a two samples t-test?

Answer 13

1. The sampling distributions of both variables that you are testing should be approximately normally distributed (the “normality” assumption)
   - Central Limit Theorem (both parent populations need to be approximately normally distributed, and/or both n is greater or equal to 30.

[The lower capital case n stands for sample size of a subgroup.]

2. The variances in the two populations should be equal (the “homogeneity of variance” assumption), SPSS runs it for us

Question 14

What does it mean that the t-test is a robust test?

Answer 14

It is relatively insensitive to violations of its underlying mathematical assumptions.

Question 15

The worn-shirt sleep efficiency experiment should use which tets?

Answer 15

Within subjects design
Paired samples t-test, to look at the magnitude of the scores

Ho: Partner scent influences sleep efficiency. Mud = 0%
H1: Partner scent does not influence sleep efficiency. Mud is not equal to 0%

The long way: the sample with Dbar-obt = 3.33% is a random sample from a population of difference scores where Mud = 0%.

Question 16

How do we calculate the effect size for the paired-sample t-test?

Answer 16

Cohen’s d = Absolute value of Dbar-obt / sigmad

But we don’t know sigma d, we put on a d hat and uses the estimated s
d hat = Absolute value of Dbar-obt / sd

Question 17

What if our two samples in the independent sample t-test are not equal in size?

Answer 17

We will use a weighted pooled standard deviation of the two samples to calculate Sxbar1- Sxbar2

The most complex formula

Question 17

If the correlated groups design is potentially more powerful, why not always use this design?

Answer 17

“First, the independent groups design is much more efficient from a df per measurement analysis. The degrees of freedom are important because the higher the df, the lower tcrit.”

“Second, many experiments preclude using the same subject in both conditions.”