M2 CONTENT Flashcards
Characteristics of the normal distribution
- A frequency distribution (histogram) of scale values
- Bell shaped (wide, or narrow)
- Symmetrical
- Unimodal
How can we use the normal distribution?
TWO WAYS
- 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)
Between -1 and 1:
- 68.26% of scores fall
- On each half = 34.13%
Between -2 and 2:
- 95.44%
- On each half = 34.13 + 13.59 (# between 1 and 2) = 47.72
Percentile
the proportion of scores that fall below a given score
Discuss the general features of a set of z scores.
- 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
Discuss the general features of sampling distributions of the mean.
- 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
Compare when to use a z score and a z statistic.
- Z score: comparing a single score to a population
- Z statistic: comparing a mean to a distribution of means (taken from the same population)
Explain the Central Limit Theorem.
- 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
What does “standard error” imply?
the variability/error/range between the means calculated from the same sample (z statistic)
Identify the similarities and differences of parametric vs. nonparametric tests.
- 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
Compare and contrast a H0 sampling distribution and a H1 sampling distribution.
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.
Explain what information effect size estimates add beyond a Null Hypothesis Significance Test result.
If we DID draw from a different population, how different is that new population’s mean from the null mean?
What can a confidence interval tell us about a mean?
If the same population is sampled repeatedly, the Cl will contain the actual population mean a percentage of the time (95%)
Explain how sample size and alpha affect confidence intervals.
Larger sample sizes result in narrower confidence intervals, while higher alpha levels (lower confidence levels) also lead to narrower intervals
Define Power (in the NHST context).
- 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)
Describe the relationships among power, effect size, sample size, and alpha.
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
List ways to increase power in a study.
Increase sample size (researcher has most control over this)
