paired difference test

(noun)

A type of location test that is used when comparing two sets of measurements to assess whether their population means differ.

Related Terms

Examples of paired difference test in the following topics:

  • 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.
    • In statistics, a paired difference test is a type of location test used when comparing two sets of measurements to assess whether their population means differ.
    • A paired difference test uses additional information about the sample that is not present in an ordinary unpaired testing situation, either to increase the statistical power or to reduce the effects of confounders.
    • $t$-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).

  • Comparing Matched or Paired Samples

    • In a hypothesis test for matched or paired samples, subjects are matched in pairs and differences are calculated.
    • When performing a hypothesis test comparing matched or paired samples, the following points hold true:
    • The differences form the sample that is used for the hypothesis test.
    • In a hypothesis test for matched or paired samples, subjects are matched in pairs and differences are calculated.
    • Construct a hypothesis test in which the data set is the set of differences between matched or paired samples.

  • Wilcoxon t-Test

    • The Wilcoxon $t$-test assesses whether population mean ranks differ for two related samples, matched samples, or repeated measurements on a single sample.
    • The Wilcoxon signed-rank t-test is a non-parametric statistical hypothesis test used when comparing two related samples, matched samples, or repeated measurements on a single sample to assess whether their population mean ranks differ (i.e., it is a paired difference test).
    • It can be used as an alternative to the paired Student's $t$-test, $t$-test for matched pairs, or the $t$-test for dependent samples when the population cannot be assumed to be normally distributed.
    • Other names may include the "$t$-test for matched pairs" or the "$t$-test for dependent samples."
    • Order the remaining pairs from smallest absolute difference to largest absolute difference, $\left| { x }_{ 2,i }-{ x }_{ 1,i } \right|$.

  • t-Test for Two Samples: Independent and Overlapping

    • Two-sample t-tests for a difference in mean involve independent samples, paired samples, and overlapping samples.
    • In the latter case the estimated t-statistic must either be tested with modified degrees of freedom, or it can be tested against different critical values.
    • Two-sample t-tests for a difference in mean involve independent samples, paired samples and overlapping samples.
    • Paired t-tests are a form of blocking, and have greater power than unpaired tests when the paired units are similar with respect to "noise factors" that are independent of membership in the two groups being compared.
    • In a different context, paired t-tests can be used to reduce the effects of confounding factors in an observational study.

  • Comparing Two Sample Averages

    • and divide by the standard error in order to standardize the difference.
    • Two-sample t-tests for a difference in mean involve independent samples, paired samples and overlapping samples.
    • Paired sample 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).
    • An overlapping sample t-test is used when there are paired samples with data missing in one or the other samples.
    • Contrast two sample means by standardizing their difference to find a t-score test statistic.

  • Quantitative or Qualitative Data?

    • Different statistical tests are used to test quantitative and qualitative data.
    • Paired and unpaired t-tests and z-tests are just some of the statistical tests that can be used to test quantitative data.
    • It can be used to determine if two sets of data are significantly different from each other and is most commonly applied when the test statistic would follow a normal distribution if the value of a scaling term in the test statistic were known.
    • A test of goodness of fit establishes whether or not an observed frequency distribution differs from a theoretical distribution, and a test of independence assesses whether paired observations on two variables, expressed in a contingency table, are independent of each other (e.g., polling responses from people of different nationalities to see if one's nationality is related to the response).
    • Plots of the t distribution for several different degrees of freedom.

  • The t-Test

    • A t-test is any statistical hypothesis test in which the test statistic follows a Student's t-distribution if the null hypothesis is supported.
    • It can be used to determine if two sets of data are significantly different from each other, and is most commonly applied when the test statistic would follow a normal distribution if the value of a scaling term in the test statistic were known.
    • A test of a null hypothesis that the difference between two responses measured on the same statistical unit has a mean value of zero.
    • This is often referred to as the "paired" or "repeated measures" t-test.
    • A test of whether the slope of a regression line differs significantly from 0.

  • Distribution-Free Tests

    • Anderson–Darling test: tests whether a sample is drawn from a given distribution.
    • McNemar's test: tests whether, in $2 \times 2$ contingency tables with a dichotomous trait and matched pairs of subjects, row and column marginal frequencies are equal.
    • Sign test: tests whether matched pair samples are drawn from distributions with equal medians.
    • Squared ranks test: tests equality of variances in two or more samples.
    • Wilcoxon signed-rank test: tests whether matched pair samples are drawn from populations with different mean ranks.

  • Using Two Samples

    • Politicians compare the proportion of individuals from different income brackets who might vote for them.
    • The parameter tested using matched pairs is the population mean (see ).
    • Tests of matched or paired samples (necessarily a test of the population mean)
    • In this section, we explore hypothesis testing of two independent population means (and proportions) and also tests for paired samples of population means.
    • Distinguish between independent and matched pairs in terms of hypothesis tests comparing two groups.

  • Introduction

    • Politicians compare the proportion of individuals from different income brackets who might vote for them.
    • The groups are classified either as independent or matched pairs.
    • Matched pairs consist of two samples that are dependent.
    • The parameter tested using matched pairs is the population mean.
    • TI-83+ and TI-84 instructions are included as well as the test statistic formulas.