When is t stat significance

Because experimentally determining it is not practical, we need to make an informed guess. For the purposes of this column, we will assume that it is normal. We will discuss robustness of tests to this assumption of normality in another column.

To complete our model of H 0 , we still need to estimate its spread. To do this we return to the concept of sampling. To estimate the spread of H 0 , we repeat the measurement of our protein's expression. Next, we make the key assumption that the s. In other words, regardless of whether the sample mean is representative of the null distribution, we assume that its spread is. This assumption of equal variances is common, and we will be returning to it in future columns.

We localize the mean expression on this distribution to calculate the P value, analogously to what was done with the single value in Figure 1c. This is called the test statistic. It turns out, however, that the shape of this sampling distribution is close to, but not exactly, normal. The extent to which it departs from normal is known and given by the Student's t distribution Fig. The test statistic described above is compared to this distribution and is thus called the t statistic.

The test illustrated in Figure 2 is called the one-sample t -test. The distribution is used to evaluate the significance of a t statistic derived from a sample of size n and is characterized by the degrees of freedom, d. This departure in distribution shape is due to the fact that for most samples, the sample variance, s x 2 , is an underestimate of the variance of the null distribution.

The distribution of sample variances turns out to be skewed. The asymmetry is more evident for small n , where it is more likely that we observe a variance smaller than that of the population. The t distribution accounts for this underestimation by having higher tails than the normal distribution Fig. As n grows, the t distribution looks very much like the normal, reflecting that the sample's variance becomes a more accurate estimate.

As a result, if we do not correct for this—if we use the normal distribution in the calculation depicted in Figure 2c —we will be using a distribution that is too narrow and will overestimate the significance of our finding.

The relationship between t and P is shown in Figure 3b and can be used to express P as a function of the quantities on which t depends D , s x , n. A more general type of calculation can identify conditions for which a test can reliably detect whether a sample comes from a distribution with a different mean.

This speaks to the test's power, which we will discuss in the next column. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. How to say if the variable is significant looking only at "t value"? Ask Question.

Asked 4 years, 11 months ago. Active 2 years, 6 months ago. Viewed 52k times. Improve this question. Nick Cox For example, the shaded region represents the probability of obtaining a t-value of 2. Imagine a magical dart that could be thrown to land randomly anywhere under the distribution curve. What's the chance it would land in the shaded region? The calculated probability is 0. In other words, the probability of obtaining a t-value of 2. How likely is that?

Not very! It's much more likely that this sample comes from different population, one with a mean greater than 5. In this way, T and P are inextricably linked.

Consider them simply different ways to quantify the "extremeness" of your results under the null hypothesis. The larger the absolute value of the t-value, the smaller the p-value, and the greater the evidence against the null hypothesis. You can verify this by entering lower and higher t values for the t-distribution in step 6 above. The t-distribution example shown above is based on a one-tailed t-test to determine whether the mean of the population is greater than a hypothesized value.

Therefore the t-distribution example shows the probability associated with the t-value of 2. How would you use the t-distribution to find the p-value associated with a t-value of 2. Therefore, it is safe to reject the null hypothesis that there is no difference between means. The population set has intrinsic differences, and they are not by chance. Financial Ratios. Tools for Fundamental Analysis. Portfolio Management. Investing Essentials. Fundamental Analysis. Your Privacy Rights.

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Explaining the T-Test. Ambiguous Test Results. T-Test Assumptions. Calculating T-Tests. Correlated or Paired T-Test. Equal Variance Pooled T-Test. Unequal Variance T-Test. Determining Which T-Test to Use. Unequal Variance T-Test Example. Key Takeaways A t-test is a type of inferential statistic used to determine if there is a significant difference between the means of two groups, which may be related in certain features.

The t-test is one of many tests used for the purpose of hypothesis testing in statistics. There are several different types of t-test that can be performed depending on the data and type of analysis required. Set 1 Set 2