Statistical Distributions Exam 1

Question 1

Normal distributions

Answer 1

• Distribution for continuous variables
• Sometimes described as the “bell curve”
• Symmetrical around the mean
• Mean, median, and mode have same value
• Curves approach the X-axis asymptotically

Question 2

Z-distributions

Answer 2

• Data have been transformed to follow the standard normal distribution
• z-score (aka standard score) describes the deviation of an observation from the mean in terms of “standard units” (or standard deviations) from zero

Question 3

T-distributions

Answer 3

• Modification of the z-distribution when the sample size is relatively small (n<30) and when the population SD is not known
• At small sample sizes, the t-distribution is flatter with thicker tails than the z-distribution
• As sample size increases the t-distribution approaches the z-distribution

Question 4

(z-) scores

Answer 4

• z-score (aka standard score) describes the deviation of an observation from the mean in terms of “standard units” (or standard deviations) from zero
• A way to transform all normal distributions so that they use the same scale
• A way of expressing any raw score in terms of standard deviation (SD) units

Question 5

central limit theorem

Answer 5

• Fundamental concept supporting most of statistical testing
• If we draw equally sized samples from a non-normal distribution, the distribution of the means of these samples will still be normal, as long as the samples are large enough

Question 6

central limit theorem three main tenets

Answer 6

• The mean of all sample means will equal the population mean
• The standard deviation of the sample means is equal to the standard error of the mean
• As the sample size increases, the distribution of the sample means approaches the normal distribution (regardless of the underlying distribution of the variable)

Question 7

Repeated sampling

Answer 7

• Concept with the central limit theorem
• Repeating a study with a different sample many times over will result in the findings approaching the true population values (e.g., mean difference)
• Supports the idea that we will be correct with our conclusions “in the long run”