Calculating and Understanding T-Tests Research Paper

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Testing and Assessment

Describe the basic characteristics of a standardized test and norms.

Standardized tests are administered and scored in a consistent manner. When standardized tests are given, conditions are held consistent and conducted in a predetermined way that is considered the standard for the test. Some of the variables that are held constant include, such as the test questions, the conditions for administering the tests, the scoring procedures and interpretations of the answers. Norms are generated by using a single test score to relate it to the test scores of other students, or by the same students at different times. Norms are generally established on a nation-wide basis on standardized tests rather than classroom tests that are made by teachers.

A test measuring basic math skills in adults is normally distributed, with mean = 20 and standard deviation = 7.

Calculate the z score and T score for each of the following test scores:

The formula for computing z-scores is:

Raw Scores

Z Scores



Score is less than the mean by more than1 standard deviation



Score is less than the mean by about 1/4 standard deviation



Score is more than the mean, by about 1/2 standard deviation



Score is more than the mean by more than1 standard deviation

This means the formula for computing standard scores is:

Or this more complex formula: t = [ x - ? ] / [ s / sqrt ( n ) ]

Raw Scores

Z Scores

T Scores













What is the usefulness of transforming raw scores to z scores or T scores? What do these numbers tell us?

Converting individual raw scores into a standardized form provides a more meaningful description of the individual scores that make up the distribution. Z scores are a conversion of individual raw scores into a standardized form that relies on the population mean and standard deviation. T scores -- also known as standardized scores -- are a conversion of individual raw scores into a standard form, and the transformation is made without knowledge of the population's mean and standard deviation. Because the population parameters are not know, the statistician must estimate them by using the best guess, which is essentially the corresponding sample statistics.

How would we go about determining percentile ranks for a score obtained on a standardized test?

In order to determine percentile ranks for scores that have been obtained on a standardized test, the data must be organized in order from lowest to highest. The rank of each datum or data point is said to represent "i" in the formula to calculate percentile ranks. The number of observations or test-takers, say, is represented by "n" in the formula. The percentile is then calculated by using this formula:

P = (100(i -- 0.5))/n


i = rank n = total number of observations

What information would we need to know?

Basically, in order to calculate the percentile ranks for scores that have been obtained on a standardized test, we need to know the standardized scores for each of test-takers and the total number of test-takers. We need to be able to rank order the standardized scores.

What would the percentile rank tell us?

A percentile on a test is the percentage of scores that are less than a particular given score. The most useful aspect of percentiles is that convert raw data, which is often difficult to understand or interpret, into a simpler form that is generally meaningful to an uninitiated viewer.

Describe the basic concepts and types of reliability and validity that apply to tests.

Types of Reliability.

In research, reliability means repeatability or consistency. As long as what is being measured does not change, a reliable measurement will produce the same result or outcome over and over again, as long as what is being measured does not change. A dependable measure has both validity and reliability. Reliability is an informed estimation and these estimations fall into four categories that look at reliability in a different way. 1) Inter-rater or inter-observer reliability is used to determine the consistency of several raters over time when they are observing the same thing and scoring what they observe. 2) Test-Retest Reliability - This estimate is used to determine some measure of consistency from one time to another time, again, by scoring or rating…[continue]

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