standardized tests

Examples of standardized tests in the following topics:

• Standardized Tests

  • A standardized test is a test that is administered and scored in a consistent manner.
  • A standardized test is a test that is administered and scored in a consistent manner.
  • Finally, critics have expressed concern that standardized tests may create testing bias.
  • Students must pass a standardized test in order to graduate from high school.
  • The most common standardized tests for applying to college are the SAT and ACT.

• Standardized Tests

  • Standardized tests are identical exams always administered in the same way so as to be able to compare outcomes across all test-takers.
  • Standardized tests are perceived as being "fairer" than non-standardized tests and more conducive to comparison of outcomes across all test takers.
  • Some recent standardized tests incorporate both criterion-referenced and norm-referenced elements in to the same test.
  • Standardized tests are often used to select students for specific programs.
  • Some standardized tests are designed specifically to assess human intelligence.

• Controversies in Intelligence and Standardized Testing

  • Intelligence tests and standardized tests face criticism for their uses and applications in society.
  • Intelligence tests and standardized tests are widely used throughout many different fields (psychology, education, business, etc.) because of their ability to assess and predict performance.
  • Another criticism lies in the use of intelligence and standardized tests as predictive measures for social outcomes.
  • Critics of standardized tests also point to problems associated with using the SAT and ACT exams to predict college success.
  • Standardized tests don't measure factors like motivational issues or study skills, which are also important for success in school.

• Student Learning Outcomes

  • Conduct and interpret hypothesis tests for two population means, population standard deviations known.
  • Conduct and interpret hypothesis tests for two population means, population standard deviations unknown.

• Student Learning Outcomes

  • Conduct and interpret hypothesis tests for a single population mean, population standard deviation known.
  • Conduct and interpret hypothesis tests for a single population mean, population standard deviation unknown.

• IQ Tests

  • IQ tests attempt to measure and provide an intelligence quotient, which is a score derived from a standardized test designed to access human intelligence.
  • After decades of revision, modern IQ tests produce a mathematical score based on standard deviation, or difference from the average score.
  • The scores of an IQ test are normally distributed so that one standard deviation is equal to 15 points; that is to say, when you go one standard deviation above the mean of 100, you get a score of 115.
  • While all of these tests measure intelligence, not all of them label their standard scores as IQ scores.
  • IQ test scores tend to form a bell curve, with approximately 95% of the population scoring between two standard deviations of the mean score of 100.

• Assumptions

  • Assumptions of a $t$-test depend on the population being studied and on how the data are sampled.
  • Most $t$-test statistics have the form $t=\frac{Z}{s}$, where $Z$ and $s$ are functions of the data.
  • where $\bar { X }$ is the sample mean of the data, $n$ is the sample size, and $\hat { \sigma }$ is the population standard deviation of the data; $s$ in the one-sample $t$-test is $\hat { \sigma } /\sqrt { n }$, where $\hat { \sigma }$ is the sample standard deviation.
  • This can be tested using a normality test, or it can be assessed graphically using a normal quantile plot.
  • If using Student's original definition of the $t$-test, the two populations being compared should have the same variance (testable using the $F$-test or assessable graphically using a Q-Q plot).

• When Does the Z-Test Apply?

  • If $T$ is a statistic that is approximately normally distributed under the null hypothesis, the next step in performing a $Z$-test is to estimate the expected value $\theta$ of $T$ under the null hypothesis, and then obtain an estimate $s$ of the standard deviation of $T$.
  • We then calculate the standard score $Z = \frac{(T-\theta)}{s}$, from which one-tailed and two-tailed $p$-values can be calculated as $\varphi(-Z)$ (for upper-tailed tests), $\varphi(Z)$ (for lower-tailed tests) and $2\varphi(\left|-Z\right|)$ (for two-tailed tests) where $\varphi$ is the standard normal cumulative distribution function.
  • To calculate the standardized statistic $Z = \frac{(X − μ_0)} {s}$ , we need to either know or have an approximate value for $\sigma^2$, from which we can calculate $s^2 = \frac{\sigma^2}{n}$.
  • The following formula converts a random variable $X$ to the standard $Z$:
  • Nuisance parameters should be known, or estimated with high accuracy (an example of a nuisance parameter would be the standard deviation in a one-sample location test).

• Comparing Two Sample Averages

  • The difference between the two samples depends on both the means and the standard deviations.
  • and divide by the standard error in order to standardize the difference.
  • A t-test is any statistical hypothesis test in which the test statistic follows Student's t distribution, as shown in , if the null hypothesis is supported.
  • These tests are widely used in commercial survey research (e.g., by polling companies) and are available in many standard crosstab software packages.
  • Contrast two sample means by standardizing their difference to find a t-score test statistic.

• t-Test for Two Samples: Paired

  • Paired-samples $t$-tests typically consist of a sample of matched pairs of similar units, or one group of units that has been tested twice.
  • $t$-tests are carried out as paired difference tests for normally distributed differences where the population standard deviation of the differences is not known.
  • Paired samples $t$-tests typically consist of a sample of matched pairs of similar units, or one group of units that has been tested twice (a "repeated measures" $t$-test).
  • Note, however, that an increase of statistical power comes at a price: more tests are required, each subject having to be tested twice.
  • Paired-samples $t$-tests are often referred to as "dependent samples $t$-tests" (as are $t$-tests on overlapping samples).