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Statistical tests for 1 or 2 samples

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INTRODUCTION

The use of statistics can be categorized as either descriptive or inferential. With inferential statistics generalizations are made about populations from samples. For example, how representative are the values calculated from a sample, how likely is the result a chance finding, and how do different groups compare? As described in the previous article by McLarty and Bahna, the basics of hypothesis testing are as follows: make a hypothesis, draw a sample, calculate a test statistic, and, based

TESTING OF MEANS (STUDENT t TEST)

Perhaps the most well known of statistical tests are the t test and the χ2 test. The t test is used to compare 2 means from independent normal distributions and the χ2 test to compare grouped data with no explicit distributional assumptions. However, the t test can also be used for a single-group comparison, comparing a mean value from a normal distribution to a single-group value. Other single-group tests include testing proportions or percentages from binomial distributions (for example,

ONE-SAMPLE t TEST

The Student t test is used to compare 2 means, that is, means in 2 different groups (say, treated or untreated), or to compare a single mean against a known constant (eg, normal temperature, average IQ). The idea behind a t test is that, under certain conditions, the mean of a sample divided by its standard error (SE) follows a known distribution, the t distribution, from which probabilities can be calculated and statistical hypotheses can be tested.

For example, assume a study was performed to

TWO-SAMPLE t TEST

The same principles apply for a 2-sample t test, and all its variants, as for the 1-sample test: a t statistic is the ratio of a mean value divided by its SE. The complication comes in estimation of the SE. The specific formula depends on whether the 2 groups being compared have the same variance and whether the sample sizes are the same in both groups. In a 2-sample test the numerator of the ratio is the absolute difference between 2 means,

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2 (ie, whether it is negative or positive). The

PAIRED t TEST

All statistical procedures have underlying assumptions. For the t test, the major assumptions are that the samples are taken from a normally distributed population and the groups being compared are independent. However, in many medical studies, groups are not independent. The most common example is before-after studies, where something is measured in the same individuals before and after an intervention of some kind. In this case, the before and after data are not independent because the same

Simple Proportions

Sometimes it is desirable with a single sample of patients to determine what proportion of them have a certain condition (eg, atopy) and to determine whether this proportion is unusually higher or lower than expected. There are several ways to go about this statistically, including binomial, multinomial, and Poisson tests. One such test presented herein is the χ2 test. For binary data (eg, yes/no data) there are better methods, but the single-group χ2 method leads didactically into the next

NONPARAMETRIC TESTS

With the exception of the χ2 test, all of the tests of hypotheses discussed herein require assumptions about the distribution of the data samples, for example, the t distribution. Means and standard errors are parameters that help specify the underlying distribution. Therefore, t tests and others like it are called parametric tests. Fortunately, many variables in nature follow a normal distribution. However, there are situations in which the underlying distribution is not normal or is not known

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Cited by (1)

  • Serum total IgE level during pregnancy and postpartum

    2011, Allergologia et Immunopathologia
    Citation Excerpt :

    Since the samples were mostly from different women, the study is primarily cross-sectional. Student's t-test was used to compare two means17 and analysis of variance was used to assess the variation between more than two means.18 In addition to the time variable, the postpartum IgE data were analysed according to the method of delivery; vaginal versus caesarean section.

Disclosures: Authors have nothing to disclose.

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