# One Tailed And Two Tailed T Test Pdf

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- “Sir, you are unethical!” One-tailed vs. Two-tailed Testing
- One- and two-tailed tests
- FAQ: What are the differences between one-tailed and two-tailed tests?
- One-tailed and two-tailed tests

## “Sir, you are unethical!” One-tailed vs. Two-tailed Testing

In statistical significance testing , a one-tailed test and a two-tailed test are alternative ways of computing the statistical significance of a parameter inferred from a data set, in terms of a test statistic.

A two-tailed test is appropriate if the estimated value is greater or less than a certain range of values, for example, whether a test taker may score above or below a specific range of scores. This method is used for null hypothesis testing and if the estimated value exists in the critical areas, the alternative hypothesis is accepted over the null hypothesis. A one-tailed test is appropriate if the estimated value may depart from the reference value in only one direction, left or right, but not both.

An example can be whether a machine produces more than one-percent defective products. In this situation, if the estimated value exists in one of the one-sided critical areas, depending on the direction of interest greater than or less than , the alternative hypothesis is accepted over the null hypothesis.

Alternative names are one-sided and two-sided tests; the terminology "tail" is used because the extreme portions of distributions, where observations lead to rejection of the null hypothesis, are small and often "tail off" toward zero as in the normal distribution , colored in yellow, or "bell curve", pictured on the right and colored in green.

One-tailed tests are used for asymmetric distributions that have a single tail, such as the chi-squared distribution , which are common in measuring goodness-of-fit , or for one side of a distribution that has two tails, such as the normal distribution , which is common in estimating location; this corresponds to specifying a direction. Two-tailed tests are only applicable when there are two tails, such as in the normal distribution, and correspond to considering either direction significant.

In the approach of Ronald Fisher , the null hypothesis H 0 will be rejected when the p -value of the test statistic is sufficiently extreme vis-a-vis the test statistic's sampling distribution and thus judged unlikely to be the result of chance.

In a one-tailed test, "extreme" is decided beforehand as either meaning "sufficiently small" or meaning "sufficiently large" — values in the other direction are considered not significant. One may report that the left or right tail probability as the one-tailed p-value, which ultimately corresponds to the direction in which the test statistic deviates from H 0. By contrast, testing whether it is biased in either direction is a two-tailed test, and either "all heads" or "all tails" would both be seen as highly significant data.

In medical testing, while one is generally interested in whether a treatment results in outcomes that are better than chance, thus suggesting a one-tailed test; a worse outcome is also interesting for the scientific field, therefore one should use a two-tailed test that corresponds instead to testing whether the treatment results in outcomes that are different from chance, either better or worse. In coin flipping, the null hypothesis is a sequence of Bernoulli trials with probability 0.

However, if testing for whether the coin is biased towards heads or tails, a two-tailed test would be used, and a data set of five heads sample mean 1 is as extreme as a data set of five tails sample mean 0. The p -value was introduced by Karl Pearson [6] in the Pearson's chi-squared test , where he defined P original notation as the probability that the statistic would be at or above a given level.

This is a one-tailed definition, and the chi-squared distribution is asymmetric, only assuming positive or zero values, and has only one tail, the upper one. It measures goodness of fit of data with a theoretical distribution, with zero corresponding to exact agreement with the theoretical distribution; the p -value thus measures how likely the fit would be this bad or worse.

The distinction between one-tailed and two-tailed tests was popularized by Ronald Fisher in the influential book Statistical Methods for Research Workers , [7] where he applied it especially to the normal distribution , which is a symmetric distribution with two equal tails. The normal distribution is a common measure of location, rather than goodness-of-fit, and has two tails, corresponding to the estimate of location being above or below the theoretical location e.

In the case of a symmetric distribution such as the normal distribution, the one-tailed p -value is exactly half the two-tailed p -value: [7]. Some confusion is sometimes introduced by the fact that in some cases we wish to know the probability that the deviation, known to be positive, shall exceed an observed value, whereas in other cases the probability required is that a deviation, which is equally frequently positive and negative, shall exceed an observed value; the latter probability is always half the former.

Fisher emphasized the importance of measuring the tail — the observed value of the test statistic and all more extreme — rather than simply the probability of specific outcome itself, in his The Design of Experiments If the test statistic follows a Student's t -distribution in the null hypothesis — which is common where the underlying variable follows a normal distribution with unknown scaling factor, then the test is referred to as a one-tailed or two-tailed t -test.

If the test is performed using the actual population mean and variance, rather than an estimate from a sample, it would be called a one-tailed or two-tailed Z -test. The statistical tables for t and for Z provide critical values for both one- and two-tailed tests. That is, they provide the critical values that cut off an entire region at one or the other end of the sampling distribution as well as the critical values that cut off the regions of half the size at both ends of the sampling distribution.

From Wikipedia, the free encyclopedia. Main article: Checking whether a coin is fair. Animal Behaviour. Educational Researcher. Dekking, Michel, London: Springer. Freund , Modern Elementary Statistics , sixth edition. Prentice hall. Philosophical Magazine. Series 5. Statistical Methods for Research Workers. Outline Index. Descriptive statistics. Mean arithmetic geometric harmonic Median Mode. Central limit theorem Moments Skewness Kurtosis L-moments.

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## One- and two-tailed tests

If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Donate Login Sign up Search for courses, skills, and videos. Math Statistics and probability Significance tests hypothesis testing More significance testing videos. Hypothesis testing and p-values.

In statistical significance testing , a one-tailed test and a two-tailed test are alternative ways of computing the statistical significance of a parameter inferred from a data set, in terms of a test statistic. A two-tailed test is appropriate if the estimated value is greater or less than a certain range of values, for example, whether a test taker may score above or below a specific range of scores. This method is used for null hypothesis testing and if the estimated value exists in the critical areas, the alternative hypothesis is accepted over the null hypothesis. A one-tailed test is appropriate if the estimated value may depart from the reference value in only one direction, left or right, but not both. An example can be whether a machine produces more than one-percent defective products.

Before you order, simply sign up for a free user account and in seconds you'll be experiencing the best in CFA exam preparation. Quantitative Methods 2 Reading Hypothesis Testing Subject 2. Null Hypothesis and Alternative Hypothesis. Seeing is believing! Find out more.

Two of these correspond to one-tailed tests and one corresponds to a we may wish to compare the mean of a sample to a given value x using a t-test. Our null.

## FAQ: What are the differences between one-tailed and two-tailed tests?

When you conduct a test of statistical significance, whether it is from a correlation, an ANOVA, a regression or some other kind of test, you are given a p-value somewhere in the output. If your test statistic is symmetrically distributed, you can select one of three alternative hypotheses. Two of these correspond to one-tailed tests and one corresponds to a two-tailed test. However, the p-value presented is almost always for a two-tailed test. But how do you choose which test?

Our websites may use cookies to personalize and enhance your experience. By continuing without changing your cookie settings, you agree to this collection. For more information, please see our University Websites Privacy Notice. The t test is one type of inferential statistics. It is used to determine whether there is a significant difference between the means of two groups.

### One-tailed and two-tailed tests

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Open topic with navigation. This function gives an unpaired two sample Student t test with a confidence interval for the difference between the means. The unpaired t method tests the null hypothesis that the population means related to two independent, random samples from an approximately normal distribution are equal Altman, ; Armitage and Berry, The unpaired t test should not be used if there is a significant difference between the variances of the two samples; StatsDirect tests for this and gives appropriate warnings. For the situation of unequal variances, StatsDirect calculates Satterthwaite's approximate t test; a method in the Behrens-Welch family Armitage and Berry,

But you don't really care about it being more effective, just that it isn't any less effective (after all, your drug is cheaper). You can run a one-tailed test to check that.

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Exploratory Data Analysis 1.

t Distribution Table. How can we tell whether it is a one-tailed or a two-tailed test? A one-tailed test looks for an “increase” or “decrease” in the parameter.

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