Loading the player...

What is a 'T-Test'

A t-test is an analysis of two populations means through the use of statistical examination; a t-test with two samples is commonly used with small sample sizes, testing the difference between the samples when the variances of two normal distributions are not known.

A t-test looks at the t-statistic, the t-distribution and degrees of freedom to determine the probability of difference between populations; the test statistic in the test is known as the t-statistic. To conduct a test with three or more variables, an analysis of variance (ANOVA) must be used.

BREAKING DOWN 'T-Test'

A form of hypothesis testing, the t-test is just one of many tests used for this purpose. Statisticians must use tests other than the t-test to examine more variables, as well as for test with larger sample sizes. For a large sample size, statisticians use a z-test. Other testing options include the chi-square test and the f-test.

Statistical Analysis of the T-Test

The formula used to calculate the test is a ratio: The top portion of the ratio is the easiest portion to calculate and understand, as it is simply the difference between the means or averages of the two samples. The lower half of the ratio is a measurement of the dispersion, or variability, of the scores. The bottom part of this ratio is known as the standard error of the difference. To compute this part of the ratio, the variance for each sample is determined and is then divided by the number of individuals the compose the sample, or group. These two values are then added together, and a square root is taken of the result.

Example

For example, consider that an analyst wants to study the amount that Pennsylvanians and Californians spend, per month, on clothing. It would not be practical to record the spending habits of every individual (or family) in both states, thus a sample of spending habits is taken from a selected group of individuals from each state. The group may be of any small to moderate size — for this example, assume that the sample group is 200 individuals.

The average amount for Pennsylvanians comes out to $500; the average amount for Californians is $1,000. The t-test questions whether the different between the groups is representative of a true difference between people in Pennsylvania and people in California in general or if it is likely a meaningless statistical difference. In this example, if, theoretically, all Pennsylvanians spent $500 per month on clothing and all Californians spent $1,000 per month on clothing, it is highly unlikely that 200 randomly selected individuals all spent that exact amount, respective to state. Thus, if an analyst or statistician yielded the results listed in the example above, it is safe to conclude that the difference between sample groups is indicative of a significant difference between the populations, as a whole, of each state.

RELATED TERMS
  1. Sampling

    A process used in statistical analysis in which a predetermined ...
  2. Sample

    A subset containing the characteristics of a larger population. ...
  3. Z-Test

    A statistical test used to determine whether two population means ...
  4. Sampling Distribution

    A probability distribution of a statistic obtained through a ...
  5. Central Limit Theorem - CLT

    A statistical theory that states that given a sufficiently large ...
  6. Systematic Sampling

    A type of probability sampling method in which sample members ...
Related Articles
  1. Investing

    What's a T-Test?

    T-Test is a term from statistics that allows for the comparison of two data populations and their means. The test is used to see if the two sets of data are significantly different from one another. ...
  2. Investing

    How Does Sampling Work?

    Sampling is a term used in statistics that describes methods of selecting a pre-defined representative number of data from a larger data population.
  3. Investing

    Explaining Standard Error

    Standard error is a statistical term that measures the accuracy with which a sample represents a population.
  4. Investing

    What is Systematic Sampling?

    Systematic sampling is similar to random sampling, but it uses a pattern for the selection of the sample.
  5. Investing

    What is a Representative Sample?

    In statistics, a representative sample accurately represents the make-up of various subgroups in an entire data pool.
  6. Investing

    Understanding the Simple Random Sample

    A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen.
  7. Investing

    Explaining the Central Limit Theorem

    Central limit theorem is a fundamental concept in probability theory.
  8. Investing

    How to Use Stratified Random Sampling

    Stratified random sampling is a technique best used with a sample population easily broken into distinct subgroups. Samples are then taken from each subgroup based on the ratio of the subgroup’s ...
  9. Investing

    Using Historical Volatility To Gauge Future Risk

    Use these calculations to uncover the risk involved in your investments.
  10. Investing

    Hypothesis Testing in Finance: Concept & Examples

    When you're indecisive about an investment, the best way to keep a cool head might be test various hypotheses using the most relevant statistics.
RELATED FAQS
  1. What assumptions are made when conducting a t-test?

    Learn what a t-test is, and discover the five standard assumptions that are made regarding the validity of sampling and data ... Read Answer >>
  2. How can a representative sample lead to sampling bias?

    Learn how using representative samples alone is not enough to make sampling bias negligible and why elements such as randomization ... Read Answer >>
  3. What's the difference between a representative sample and a convenience sample?

    Learn the difference between convenience sampling and representative sampling and the advantages and disadvantages of each ... Read Answer >>
  4. What percentage of the population do you need in a representative sample?

    Learn about representative samples and how they are used in conjunction with other strategies to create useful data with ... Read Answer >>
  5. What are some common financial sampling methods?

    Read about the differences between various common financial sampling methods for financial analysts, statisticians, marketers ... Read Answer >>
  6. What is the difference between systematic sampling and cluster sampling?

    Learn about the differences between systematic sampling and cluster sampling, including how the samples are created for each ... Read Answer >>
Hot Definitions
  1. Magna Cum Laude

    An academic level of distinction used by educational institutions to signify an academic degree which was received "with ...
  2. Cover Letter

    A written document submitted with a job application explaining the applicant's credentials and interest in the open position. ...
  3. 403(b) Plan

    A retirement plan for certain employees of public schools, tax-exempt organizations and certain ministers. Generally, retirement ...
  4. Master Of Business Administration - MBA

    A graduate degree achieved at a university or college that provides theoretical and practical training to help graduates ...
  5. Liquidity Event

    An event that allows initial investors in a company to cash out some or all of their ownership shares and is considered an ...
  6. Job Market

    A market in which employers search for employees and employees search for jobs. The job market is not a physical place as ...
Trading Center