Statistics: Raw Scores and Z-scores

The original score obtained from a test or assessment, before any modifications or transformations.

A transformed score that indicates a specific score's position within a distribution by showing how many standard deviations it is above or below the mean.

The average score in a distribution.

A measure of how spread out the scores are in a distribution.

The spread within one standard deviation of the mean. In IQ testing, this range typically includes 68% of the population.

The spread within two standard deviations of the mean. In IQ testing, this range typically includes 95% of the population.

The extreme ends of the IQ distribution, typically representing 2% of the population.

Z-scores transform raw scores into a standardized format, allowing for meaningful comparisons between different distributions.

The shape of the original distribution is preserved when scores are transformed into z-scores.

The mean of the z-score distribution is always zero.

A z-score is calculated by subtracting the mean from the score and dividing by the standard deviation.

The probability of an outcome is the proportion of times it's expected to occur out of all possible outcomes.

Classical probability assumes all outcomes are equally likely, like flipping a fair coin.

Empirical probability is based on observed data, like the frequency of winning a lottery.

Subjective probability is based on personal judgment, often used for uncertain events like a sports team winning.

The hypothesis that there is no difference or relationship between variables in a population.

The hypothesis that there is a change, difference, or relationship between variables in a population.

The process of evaluating the credibility of the null hypothesis using data collected from a sample.

The probability of making a Type I error in hypothesis testing. This occurs when the null hypothesis is incorrectly rejected, even though it is true.

A Type I error occurs when you reject the null hypothesis even though it is true.

A Type II error occurs when you fail to reject the null hypothesis even though it is false.

The range of values within which the true population parameter is likely to fall, based on the sample data.

A value that is considered significantly different from the null hypothesis, based on the alpha level.

Probability is the likelihood of a future event occurring. Statistics analyzes data from past events.

A probability distribution is a mathematical function that describes the likelihood of different outcomes for a random variable. It's used in statistical analysis to understand the variability of data.

A random sample is a subset of a population where every member has an equal chance of being selected, ensuring that the sample represents the population accurately.

A percentile rank represents the percentage of individuals in a distribution who scored at or below a particular score.

A percentile is a specific value in a distribution that marks a certain percentage of the data. It corresponds to the percentile rank.

The goal of a hypothesis test is to determine if there is enough evidence to reject the null hypothesis and conclude that the treatment has a significant effect.

The set of values for the test statistic that would lead to rejecting the null hypothesis. If the calculated test statistic falls within this region, it indicates that the observed data is sufficiently extreme under the null hypothesis, prompting rejection of the null hypothesis.

A type of hypothesis test where the researcher specifies the expected direction of the effect or relationship between variables. For example, it may state that one variable is greater than or less than another variable, indicating a clear expected outcome (e.g., "As sleep deprivation increases, cognitive performance decreases").

A directional test that evaluates whether a parameter is less than a certain value. Tests the left tail of the distribution.

A directional test that evaluates whether a parameter is greater than a certain value. Tests the right tail of the distribution.

A statistical test that checks if a parameter differs significantly from a specific value, without specifying direction. It looks for both increases and decreases.

A measure that quantifies the size or strength of the effect or difference between two variables or groups.

A standardized measure of the difference between two means, showing how many standard deviations separate them.

A one-tailed test is appropriate when you have a strong theoretical basis or prior evidence suggesting that an effect will occur in one direction.

A two-tailed test is appropriate when you want to detect any significant difference, regardless of direction. This is common in exploratory research.

A large effect size indicates a large difference between groups or a strong relationship between variables, suggesting practical significance. A small effect size indicates a limited practical application.