raw score

(noun)

an original observation that has not been transformed to a $z$-score

Related Terms

Examples of raw score in the following topics:

  • Z-Scores and Location in a Distribution

    • A raw score is an original datum, or observation, that has not been transformed.
    • The conversion of a raw score, $x$, to a $z$-score can be performed using the following equation:
    • The absolute value of $z$ represents the distance between the raw score and the population mean in units of the standard deviation.
    • $z$ is negative when the raw score is below the mean and positive when the raw score is above the mean.
    • Define $z$-scores and demonstrate how they are converted from raw scores

  • Change of Scale

    • It is a dimensionless quantity obtained by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation.
    • Standard scores are also called $z$-values, $z$-scores, normal scores, and standardized variables.
    • The absolute value of $z$ represents the distance between the raw score and the population mean in units of the standard deviation.
    • $z$ is negative when the raw score is below the mean, positive when above.
    • Includes: standard deviations, cumulative percentages, percentile equivalents, $Z$-scores, $T$-scores, and standard nine.

  • Exercises

    • If you are told only that you scored in the 80th percentile, do you know from that description exactly how it was calculated?
    • The formula for finding each student's test grade (g) from his or her raw score (s) on a test is as follows: g=16+3s.
    • If a student got a raw score of 20, what is his test grade?
    • What is more likely to have a skewed distribution: time to solve an anagram problem (where the letters of a word or phrase are rearranged into another word or phrase like "dear" and "read" or "funeral" and "real fun") or scores on a vocabulary test?

  • Partitioning the Sums of Squares

    • It is sometimes convenient to use formulas that use deviation scores rather than raw scores.
    • Deviation scores are simply deviations from the mean.
    • Therefore, the score, y indicates the difference between Y and the mean of Y.
    • The next-to-last column, Y-Y', contains the actual scores (Y) minus the predicted scores (Y').
    • The sum of squares predicted is the sum of the squared deviations of the predicted scores from the mean predicted score.

  • Exercises

    • Find the deviation scores for Variable A that correspond to the raw scores of 2 and 8.
    • Find the deviation scores for Variable B that correspond to the raw scores of 5 and 4.
    • Just from looking at these scores, do you think these variables are positively or negatively correlated?
    • The correlation between the test scores is 0.6.
    • (AM) What is the correlation between the Control-In and Control-Out scores?

  • Normal distribution exercises

    • (g) Explain why simply comparing her raw scores from the two sections would lead to the incorrect conclusion that she did better on the Quantitative Reasoning section.
    • What do these Z scores tell you?
    • (a) The score of a student who scored in the 80th percentile on the Quantitative Reasoning section.
    • (b) The score of a student who scored worse than 70% of the test takers in the Verbal Reasoning section.
    • (g) We cannot compare the raw scores since they are on different scales.

  • Distributions of random variables solutions

    • (c) She scored 1.33 standard deviations above the mean on the Verbal Reasoning section and 0.57 standard deviations above the mean on the Quantitative Reasoning section. ( d) She did better on the Verbal Reasoning section since her Z score on that section was higher.
    • (g) We cannot compare the raw scores since they are on different scales.
    • Comparing her percentile scores is more appropriate when comparing her performance to others.
    • (h) Answer to part (b) would not change as Z scores can be calculated for distributions that are not normal.

  • Standard Normal Distribution

    • If all the values in a distribution are transformed to Z scores, then the distribution will have a mean of 0 and a standard deviation of 1.

  • Glossary

    • That is, two scores per subject.
    • To convert data to deviation scores typically means to subtract the mean score from each other score.
    • The transformation from a raw score X to a z score can be done using the following formula:
    • The transformation from a raw score X to a standard score can be done using the following formula:
    • The transformation from a raw score X to a z score can be done using the following formula:

  • Two sample t test

    • To evaluate the hypotheses in Exercise 5.28 using the t distribution, we must first verify assumptions. ( a) Does it seem reasonable that the scores are independent within each group?
    • (c) Do you think scores from the two groups would be independent of each other (i.e. the two samples are independent)?
    • In this case, we are estimating the true difference in average test scores using the sample data, so the point estimate is $\bar{x}_A-\bar{x}_B$ = 5.3.
    • 5.29: (a) It is probably reasonable to conclude the scores are independent.
    • The data are very limited, so we can only check for obvious outliers in the raw data in Figure 5.22.