What is the T&D delivery system for online instruction
What is the t-distribution?The t-distribution describes the standardized distances of sample means to the population mean when the population standard deviation is not known, and the observations come from a normally distributed population. Show
Is the t-distribution the same as the Student’s t-distribution?Yes. What’s the key difference between the t- and z-distributions?The standard normal or z-distribution assumes that you know the population standard deviation. The t-distribution is based on the sample standard deviation. t-Distribution vs. normal distributionThe t-distribution is similar to a normal distribution. It has a precise mathematical definition. Instead of diving into complex math, let’s look at the useful properties of the t-distribution and why it is important in analyses.
Consider the following graph comparing three t-distributions with a standard normal distribution: Figure 1: Three t-distributions and a standard normal (z-) distribution. All of the distributions have a smooth shape. All are symmetric. All have a mean of zero. The shape of the t-distribution depends on the degrees of freedom. The curves with more degrees of freedom are taller and have thinner tails. All three t-distributions have “heavier tails” than the z-distribution. You can see how the curves with more degrees of freedom are more like a z-distribution. Compare the pink curve with one degree of freedom to the green curve for the z-distribution. The t-distribution with one degree of freedom is shorter and has thicker tails than the z-distribution. Then compare the blue curve with 10 degrees of freedom to the green curve for the z-distribution. These two distributions are very similar. A common rule of thumb is that for a sample size of at least 30, one can use the z-distribution in place of a t-distribution. Figure 2 below shows a t-distribution with 30 degrees of freedom and a z-distribution. The figure uses a dotted-line green curve for z, so that you can see both curves. This similarity is one reason why a z-distribution is used in statistical methods in place of a t-distribution when sample sizes are sufficiently large. Figure 2: z-distribution and t-distribution with 30 degrees of freedom Tails for hypotheses tests and the t-distributionWhen you perform a t-test, you check if your test statistic is a more extreme value than expected from the t-distribution. For a two-tailed test, you look at both tails of the distribution. Figure 3 below shows the decision process for a two-tailed test. The curve is a t-distribution with 21 degrees of freedom. The value from the t-distribution with α = 0.05/2 = 0.025 is 2.080. For a two-tailed test, you reject the null hypothesis if the test statistic is larger than the absolute value of the reference value. If the test statistic value is either in the lower tail or in the upper tail, you reject the null hypothesis. If the test statistic is within the two reference lines, then you fail to reject the null hypothesis. Figure 3: Decision process for a two-tailed test For a one-tailed test, you look at only one tail of the distribution. For example, Figure 4 below shows the decision process for a one-tailed test. The curve is again a t-distribution with 21 degrees of freedom. For a one-tailed test, the value from the t-distribution with α = 0.05 is 1.721. You reject the null hypothesis if the test statistic is larger than the reference value. If the test statistic is below the reference line, then you fail to reject the null hypothesis. Figure 4: Decision process for a one-tailed test How to use a t-tableMost people use software to perform the calculations needed for t-tests. But many statistics books still show t-tables, so understanding how to use a table might be helpful. The steps below describe how to use a typical t-table.
What is the T used for?In English, it is most commonly used to represent the voiceless alveolar plosive, a sound it also denotes in the International Phonetic Alphabet. It is the most commonly used consonant and the second most commonly used letter in English-language texts.
What does the t tell you?The t-value measures the size of the difference relative to the variation in your sample data. Put another way, T is simply the calculated difference represented in units of standard error. The greater the magnitude of T, the greater the evidence against the null hypothesis.
What does the T measure?A t-test measures the difference in group means divided by the pooled standard error of the two group means.
What is the tThe t-value, or t-score, is a ratio of the difference between the mean of the two sample sets and the variation that exists within the sample sets. The numerator value is the difference between the mean of the two sample sets.
|