Chapter 10

Question 1

What is the t-score?

Answer 1

A T-score represents how much a specific value deviates from the mean of its distribution, expressed in relation to an unbiased estimate of the standard deviation (the standard error).

Question 2

Define unbiased parameter.

Answer 2

Unbiased estimate: An estimate of a parameter that, on average, exactly
equals the value of the parameter

Question 3

What are the characteristics of t-distribution and normal have in common?

Answer 3

1. They are symmetrical.
2. They are unimodal.
3. They have means of zero.

Question 4

What does the shape of the t distribution depend on?

Answer 4

Shape of t distribution depends on degrees of freedom (df)

Question 5

The difference between the normal and the t distribution is mainly in the
__________.

Answer 5

The difference between the normal and the t distribution is mainly in the
tails. The t distribution is leptokurtic (i.e., more peaked) and tends to have more
area in the tails than does the normal distribution.

Question 6

When to use single means?

Answer 6

One-sample t-test: When you want to test if the mean of a sample is different from a known value (e.g., the population mean).

Question 7

When to use dependant and independent means?

Answer 7

Independent means: Used when comparing two different, unrelated groups.

Dependent means: Used when comparing measurements from the same group at different points or under different conditions.

Question 8

Differentiate between within and between participant designs.

Answer 8

Within-participants design: The same participants serve in both the control
group and the treatment group

Between-participants design: Different participants are randomly assigned
to the control and treatment group

Question 9

What is matched group design?

Answer 9

Matched-groups design: Participants are matched on some variable related to
the response measure.

Students are paired based on similar past math scores. One student from each pair is taught with Method A, and the other with Method B.

Question 10

Advantages of matched group designs?

Answer 10

• Reduces variability between groups.
• Controls for confounding variables.
• Produces more reliable results.
• Requires fewer participants.

Question 11

What advantages of within participant groups?

Answer 11

• Valuable in Social Sciences: Reduces participant variability.
• Sensitive to the Null: More accurate despite fewer degrees of freedom.
• Lower Error Term: Reducing error impacts results more than degree loss.

Question 12

What is the disadvantage of within participant groups?

Answer 12

There are situations, however, where within-participants designs should not
be used. Sometimes the performance of the control task carries over to the
experimental task.

Question 13

Differentiate between z score and t score.

Answer 13

t score: The deviation of a particular value from the mean of its distribution expressed in relationship to an unbiased estimate of the standard deviation of that distribution

z score: The deviation of a particular value from the mean of its distribution
expressed in relationship to the standard deviation of that distribution

Question 14

Why is the z distrubution a normal shape?

Answer 14

The z distribution is normal in shape because m and s are fixed (and therefore don’t affect the shape) and the sample means are normally distributed or close to it (remember the central limit theorem).

Question 15

The variability of the standard error is directly affected by sample __________

Answer 15

The variability of the standard error is directly affected by sample size—smaller samples produce greater variability.

Question 16

define degrees of freedom

Answer 16

Degrees of freedom (df): The number of values free to vary once certain con
straints have been placed on data; important in several statistical procedures

Question 17

When to use t distribution?

Answer 17

when standard deviation is not known.

Question 18

What is the homogeneity of variance?

Answer 18

A further assumption with t tests for the difference between means is that the populations from which the two samples were collected have equal variability. This is called the assumption of homogeneity of variance

Question 19

Differentiate between type 1 and 2 errors and give their probabilities.

Answer 19

A Type I error occurs when you reject the null hypothesis (h0) when it is actually true.
- The probability of making a Type I error is denoted by α, which is the significance level of the test (commonly set at 0.05 or 5%)

Type II error occurs when you fail to reject the null hypothesis when it is actually false.

Probability: The probability of making a Type II error is denoted by b The value of
𝛽 depends on factors like sample size, effect size, and variability.

Question 20

What is power?

Answer 20

The power of a statistical test is the probability of correctly rejecting the null hypotheses when it is false. In other words, it is the ability of the test to detect a true effect.
Probability: Power is calculated as 1−β, where b is the probability of a Type II error.