Statistical z Score Formula

Defining Outliers using z Scores

Usefulness of z Scores

Formula for the z Score

Importance of z Scores

In statistical analysis for psychological research, what does a z score indicate about a particular raw score?

In a psychological study, researchers calculated z scores for participants' performance on a memory task. Arrange the following participants in order from the highest score to the lowest score based on their relative position in the distribution.

A psychologist is analyzing how various statistical adjustments to a research dataset affect the resulting standardized scores. Match each statistical change with its specific impact on the participants' $z$ scores.

A researcher is comparing a student's performance on two different psychological assessments that use different measurement scales. The researcher concludes that because the student achieved a $z$ score of $+2.1$ on the first assessment and a $z$ score of $+1.5$ on the second, the student's relative standing is higher on the first assessment. This conclusion is statistically valid.

In psychological research, what is the primary function of converting a raw score into a $z$ score?

Match each $z$ score with the statement that accurately describes its relative location in a distribution of psychology test scores.

In a psychological study on social anxiety, the sample mean is 50 and the standard deviation is 10. A participant who receives a raw score of 35 on this assessment has a z-score of _____.

In a psychological study on stress, researchers measure salivary cortisol levels in participants after a public speaking task. The sample distribution of cortisol has a mean of $6.0\text{ nmol/L}$ and a standard deviation of $1.5\text{ nmol/L}$. If a participant's salivary cortisol level is $9.0\text{ nmol/L}$, their corresponding $z$ score is $+2.00$.

A developmental psychologist is analyzing a child's cognitive profile across four subtests of an attention assessment, each with its own normative mean and standard deviation ($\text{SD}$). To compare these different scales, the psychologist must calculate $z$ scores for each subtest.

Arrange the child's subtest performances in order of their relative standing in the group, from the lowest relative standing (most below-average) to the highest relative standing (most above-average).

A clinical psychologist is evaluating a client's performance on two standardized neuropsychological assessments to determine which cognitive domain is more severely impaired:

• Assessment A (Attention): Mean ($M$) = $100$, Standard Deviation ($SD$) = $15$. The client's raw score is $85$.
• Assessment B (Working Memory): Mean ($M$) = $50$, Standard Deviation ($SD$) = $5$. The client's raw score is $40$.

The clinician concludes that the client has a more severe impairment in Attention because their raw score on Assessment A is further below its respective mean in raw points ($15$ points below) compared to Assessment B ($10$ points below).

By evaluating the client's performance using standardized $z$ scores, we find that the clinician's conclusion is ________ (enter 'valid' or 'invalid').