M2 CONTENT

Question 1

Characteristics of the normal distribution

Answer 1

• A frequency distribution (histogram) of scale values
• Bell shaped (wide, or narrow)
• Symmetrical
• Unimodal

Question 2

How can we use the normal distribution?

TWO WAYS

Answer 2

• Compare one raw score to a distribution of other raw scores (Z score)
• Compare one sample’s mean score to a distribution of other possible sample mean scores (Z statistic)

Question 3

Between -1 and 1:

Answer 3

• 68.26% of scores fall
• On each half = 34.13%

Question 4

Between -2 and 2:

Answer 4

• 95.44%
• On each half = 34.13 + 13.59 (# between 1 and 2) = 47.72

Question 5

Percentile

Answer 5

the proportion of scores that fall below a given score

Question 6

Discuss the general features of a set of z scores.

Answer 6

• The mean of a distribution of z scores is always 0
• The SD of a distribution of z scores is always 1; Divides by SD, which puts deviation scores in the “units” of SD
• The distribution of z scores is the same shape as its corresponding set of raw scores; Negative skew, positive skew, bell curve

Question 7

Discuss the general features of sampling distributions of the mean.

Answer 7

• Its a frequency distribution of means (rather than a frequency distribution of scores; Those means are calculated by drawing an infinite number of n-sized samples, calculating the mean for each sample, and plotting it
• Its mean, denoted um, = the mean of the population (u); Both are the same - but SAMPLING DISTRIBUTION OF THE MEAN distinguished by um
• Its SD equals the SD of the raw score population divided by the square root of the sample size; Denoted om, called the standard error of mean

Question 8

Compare when to use a z score and a z statistic.

Answer 8

• Z score: comparing a single score to a population
• Z statistic: comparing a mean to a distribution of means (taken from the same population)

Question 9

Explain the Central Limit Theorem.

Answer 9

• A distribution of sample means is normally shaped, even when the population distribution is not normal (as long as the sample size is at least ~30). So we use the normal distribution to model it
• CENTRAL LIMIT THEOREM - when sample size increases, the shape of the distribution increases

Question 10

What does “standard error” imply?

Answer 10

the variability/error/range between the means calculated from the same sample (z statistic)

Question 11

Identify the similarities and differences of parametric vs. nonparametric tests.

Answer 11

• Both used for hypothesis testing, but they differ in their assumptions about the underlying population distribution.
• Parametric tests assume a specific distribution, typically normal, while nonparametric tests make fewer or no assumptions about the distribution

Question 12

Compare and contrast a H0 sampling distribution and a H1 sampling distribution.

Answer 12

The H0 sampling distribution is the basis for determining if the observed sample statistic is likely to have occurred if the null hypothesis were true, while the H1 sampling distribution is used to understand what the expected value of the sample statistic would be if the alternative hypothesis were true.

Question 13

Explain what information effect size estimates add beyond a Null Hypothesis Significance Test result.

Answer 13

If we DID draw from a different population, how different is that new population’s mean from the null mean?

Question 14

What can a confidence interval tell us about a mean?

Answer 14

If the same population is sampled repeatedly, the Cl will contain the actual population mean a percentage of the time (95%)

Question 15

Explain how sample size and alpha affect confidence intervals.

Answer 15

Larger sample sizes result in narrower confidence intervals, while higher alpha levels (lower confidence levels) also lead to narrower intervals

Question 16

Define Power (in the NHST context).

Answer 16

• If the null is really false, how likely is it that we’re going to find a “significant effect” in our sample?
• The ability to detect an effect (if it exists)

Question 17

Describe the relationships among power, effect size, sample size, and alpha.

Answer 17

How big your sample is
* Smaller - more overlap (EX: 20)
* Larger - less overlap (EX: 100)

How far away the real distribution is from the null hypothesis distribution
* Larger effect size = larger numerator, more power

How big your alpha is
* Larger alpha = smaller critical value, more power

Question 18

List ways to increase power in a study.

Answer 18

Increase sample size (researcher has most control over this)