Week 6

Question 1

Describe the circumstances in which a t statistic is used for hypothesis testing instead of a z-score.

Answer 1

A t-statistic is used when the population mean and population standard deviation are unknown.

Question 2

Explain the fundamental difference between a t statistic and a z-score.

Answer 2

The formula is the same with the exception of using sM in the denominator as opposed to σM.

Question 3

Explain the relationship between the t distribution and the normal distribution.

Answer 3

The greater the value of df for a sample, the better the sample variance (s²) represents the population variance (σ²) and the better the t statistic approximates the z-score.

Question 4

What does sM represent? and how is it calculated?

Answer 4

Estimated standard error, (when σ is unknown).

Formula: sM = The square root of (s²/n)

Question 5

What is the t-statistic formula?

Answer 5

t = M - μ/sM

Question 6

What is a t distribution?

Answer 6

Complete set of t values computed for every possible random sample for a specific sample size (n) or a specific degrees of freedom (df).

Question 7

What causes t distributions to be flatter and more varied compared to z-score distributions?

Answer 7

Low degree of freedom (small sample).

Question 8

Two basic assumptions are necessary for hypothesis tests with the t statistic, what are they?

Answer 8

1. The values in the sample must consist of independent observations (random sampling fixes this).
2. The population sampled must be normal (or large).

Question 9

If you increase sample variance, what happens to the t statistic?

Answer 9

It decreases.

Question 10

What is Cohen’s d formula? what does it measure?

Answer 10

Cohen’s d = μ1 - μ2/σ.

It measures effect size in terms of population mean and standard deviation.

Question 11

What is the estimated d formula? what is it?

Answer 11

Estimated d = M - μ/s.

It measures estimated effect size, when population mean and standard deviation are not available.

Question 12

What does r² represent? (sometimes denoted as ω²)

Answer 12

Percentage of variance accounted for by the treatment, measures effect size.

Question 13

What is the formula for r² (ω²)?

Answer 13

r² = t²/t²+df.

Question 14

What r² values did Cohen suggest were small, medium and large treatment effects?

Answer 14

Small: 0.01
Medium: 0.09
Large: 0.25

Question 15

What is a confidence interval?

Answer 15

A range of values centred around a sample statistic that we can be X% sure the population mean falls in.

Question 16

What is the confidence interval formula?

Answer 16

μ = M ± tsM.

t is the estimated t values

Question 17

How do you estimate the t-values when you do not know the population mean?

Answer 17

1. Identify the df.
2. Choose confidence level, X%.
3. The t-values that boarder the range of X% of t values in a t-table are your estimated t-values.

Question 18

What are the two main characteristics of the confidence interval?

Answer 18

1. Wider confidence interval = the more certainty, but less precision. Smaller confidence interval = more precise, less certainty.
2. Bigger sample = smaller interval.

Question 19

What is a binomial test?

Answer 19

A hypothesis testing method used with categorical data.

Question 20

How do you preform a binomial test in SPSS?

Answer 20

Analyse → Nonparametric Tests → Legacy Dialogs → Binomial (set test proportion and cut point).

Question 21

What is the formula for the confidence interval of population proportion?

Answer 21

p = (p̂ ± z * 𝜎p̂).

will give two values

Question 22

What is the z-score formula for proportions?

Answer 22

z (for proportions) = p̂-p/𝜎p̂.

Question 23

What is the critical-t value?

Answer 23

The cut-off values for likely scores.

Question 24

What happens to the t-statistic when the sample size is increased?

Answer 24

It increases.

Question 25

What happens to the t-statistic when the sM changes?

Answer 25

Higher sM = Lower t-statistic.

Lower sM = Higher t-statistic.

Question 26

What did Cohen suggest were small, medium and large effects for d? (Cohen’s d).

Answer 26

Small = 0.20
Medium = 0.50
Large = 0.80

Question 27

How do you calculate tsM when you do NOT know the sample size, sample variance or sample SD?

Answer 27

tsM = upper/lower interval - M.

the tsM is the difference between the sample mean and the upper/lower interval