4 Stats - Normal Distribution and Z-Scores

What are the two reasons for studying distributions of scores in psychology?

• To classify data as either parametric or non-parametric.

• To explain the distribution of scores and compare distributions across groups.

• To identify outliers and compare variance.

• To determine standard deviations and medians.

What is the most common type of distribution seen in nature?

• Skewed distribution.

• Bimodal distribution.

• Normal distribution.

• Poisson distribution.

What property of the normal distribution allows calculation of probabilities?

• Knowing the mean and standard deviation enables calculation of cumulative probabilities.

• Its symmetry.

• Its bell shape.

• The height of its peak.

What is a key assumption of most inferential statistical tests?

• That data are positively skewed.

• That the data are normally distributed.

• That the median equals the mode.

• That the distribution has no outliers.

Why might normally distributed data not always be realistic?

• Sampling procedures are rarely perfect.

• The standard deviation is usually too large.

• Outliers tend to dominate distributions.

• Most variables are bimodal.

What does the Central Limit Theorem state about sampling distributions of means?

• They contain no variability.

• They approximate a normal curve regardless of the underlying variable distribution.

• They follow a bimodal curve if the population data are skewed.

• They have a mean larger than the population mean.

What is a sampling distribution?

• A frequency distribution of standardized scores.

• A distribution of means from multiple random samples of the same population.

• A curve that compares medians across samples.

• A dataset containing raw scores from a sample.

What is a key feature of a normal distribution curve?

• It is skewed to the right.

• It has no variability.

• It is symmetrical and bell-shaped.

• It contains equal proportions of z-scores and raw scores.

What is a z-score?

• A ratio of mean to median.

• A value that identifies an outlier.

• A standardized score expressed in terms of standard deviation units.

• A raw score in a normal distribution.

Why are z-scores useful?

• They calculate probabilities of medians.

• They identify whether a dataset is skewed or kurtotic.

• They provide the raw score's rank within a dataset.

• They allow comparison of scores on different scales and locate an individual’s position within a distribution.