How to Calculate a Two-Tailed Test

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In inferential statistics, hypotheses are formed as tentative answers to research questions. Statistical hypothetical testing allows us to evaluate hypotheses about population parameters based on sample statistics. The type of testing varies according to the level of measurement of the variables involved. If a population parameter is hypothesized to be greater than or less than some value, a one-tailed test is used. When no direction is indicated in the research hypothesis, a two-tailed test is used. A two-tailed test will show whether or not there is a difference in the values of the variables involved.

    Gather the data for the population parameters. Determine if there is a theoretical basis which indicates a specified difference in direction for the parameters. A specified difference would be indicated by stating that the value of one variable is higher or lower than that of the other variable. This information allows you to decide if a two-tailed test is appropriate.

    Make assumptions regarding the variable’s level of measurement, the method of sampling, the sample size, and the population parameters. Use these assumptions to formulate your hypotheses. Your first hypothesis will be your research hypothesis, or H1. This hypothesis states the difference in the variables of the population parameter. Your second hypothesis will be your null hypothesis, or H0. This hypothesis contradicts the research hypothesis and states that there is no difference between the population mean and a specified value.

    Calculate the test statistics of alpha. Alpha is the level of probability at which the null hypothesis is rejected. The alpha is customarily set at the .05, .01, or .001 levels, meaning that there will be a margin of error of 5%, 1%, or .1%. For a two-tailed test, divide the value of alpha by 2 and compare it with the Z-statistic if the standard deviation is known or the t-statistic if the standard deviation is not known.

    Test the null hypothesis to determine if there is a difference between the population parameter. The objective is to reject the null hypothesis in order to provide support for the research hypothesis. When the probability value is less than the alpha, we reject the null hypothesis and support the research hypothesis. When the probability value is greater than the alpha, we fail to reject the null hypothesis.

    Things You'll Need

    • Data for the population variables being tested
    • Calculator
    • Standard normal table
    • T-table


    • Sample sizes that are too small may skew your research results.


About the Author

Nico Riley has been a professional writer since 2006 with work appearing on various websites. Riley holds an associate degree in criminal justice from Harold Washington College and a Bachelor of Arts in sociology from the University of Illinois at Chicago. She enjoys writing on topics about society, culture, health, self-help and entertainment.

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