Week 6 Flashcards
Describe the circumstances in which a t statistic is used for hypothesis testing instead of a z-score.
A t-statistic is used when the population mean and population standard deviation are unknown.
Explain the fundamental difference between a t statistic and a z-score.
The formula is the same with the exception of using sM in the denominator as opposed to σM.
Explain the relationship between the t distribution and the normal distribution.
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.
What does sM represent? and how is it calculated?
Estimated standard error, (when σ is unknown).
Formula: sM = The square root of (s²/n)
What is the t-statistic formula?
t = M - μ/sM
What is a t distribution?
Complete set of t values computed for every possible random sample for a specific sample size (n) or a specific degrees of freedom (df).
What causes t distributions to be flatter and more varied compared to z-score distributions?
Low degree of freedom (small sample).
Two basic assumptions are necessary for hypothesis tests with the t statistic, what are they?
- The values in the sample must consist of independent observations (random sampling fixes this).
- The population sampled must be normal (or large).
If you increase sample variance, what happens to the t statistic?
It decreases.
What is Cohen’s d formula? what does it measure?
Cohen’s d = μ1 - μ2/σ.
It measures effect size in terms of population mean and standard deviation.
What is the estimated d formula? what is it?
Estimated d = M - μ/s.
It measures estimated effect size, when population mean and standard deviation are not available.
What does r² represent? (sometimes denoted as ω²)
Percentage of variance accounted for by the treatment, measures effect size.
What is the formula for r² (ω²)?
r² = t²/t²+df.
What r² values did Cohen suggest were small, medium and large treatment effects?
Small: 0.01
Medium: 0.09
Large: 0.25
What is a confidence interval?
A range of values centred around a sample statistic that we can be X% sure the population mean falls in.
What is the confidence interval formula?
μ = M ± tsM.
t is the estimated t values
How do you estimate the t-values when you do not know the population mean?
- Identify the df.
- Choose confidence level, X%.
- The t-values that boarder the range of X% of t values in a t-table are your estimated t-values.
What are the two main characteristics of the confidence interval?
- Wider confidence interval = the more certainty, but less precision. Smaller confidence interval = more precise, less certainty.
- Bigger sample = smaller interval.
What is a binomial test?
A hypothesis testing method used with categorical data.
How do you preform a binomial test in SPSS?
Analyse → Nonparametric Tests → Legacy Dialogs → Binomial (set test proportion and cut point).
What is the formula for the confidence interval of population proportion?
p = (p̂ ± z * 𝜎p̂).
will give two values
What is the z-score formula for proportions?
z (for proportions) = p̂-p/𝜎p̂.
What is the critical-t value?
The cut-off values for likely scores.
What happens to the t-statistic when the sample size is increased?
It increases.
What happens to the t-statistic when the sM changes?
Higher sM = Lower t-statistic.
Lower sM = Higher t-statistic.
What did Cohen suggest were small, medium and large effects for d? (Cohen’s d).
Small = 0.20 Medium = 0.50 Large = 0.80
How do you calculate tsM when you do NOT know the sample size, sample variance or sample SD?
tsM = upper/lower interval - M.
the tsM is the difference between the sample mean and the upper/lower interval
