What Is a T-Distribution?

The t-distribution, also known as the Student’s t-distribution, is a type of probability distribution that is similar to the normal distribution with its bell shape but has heavier tails. It is used for estimating population parameters for small sample sizes or unknown variances. T-distributions have a greater chance for extreme values than normal distributions, and as a result have fatter tails.

The t-distribution is the basis for computing t-tests in statistics.

What Does a T-Distribution Tell You? 

Tail heaviness is determined by a parameter of the t-distribution called degrees of freedom, with smaller values giving heavier tails, and with higher values making the t-distribution resemble a standard normal distribution with a mean of 0 and a standard deviation of 1.

When a sample of n observations is taken from a normally distributed population having mean M and standard deviation D, the sample mean, m, and the sample standard deviation, d, will differ from M and D because of the randomness of the sample.

A z-score can be calculated with the population standard deviation as Z = (x – M)/D, and this value has the normal distribution with mean 0 and standard deviation 1. But when using the estimated standard deviation, a t-score is calculated as T = (m – M)/{d/sqrt(n)}, and the difference between d and D makes the distribution a t-distribution with (n – 1) degrees of freedom rather than the normal distribution with mean 0 and standard deviation 1. 

Example of How to Use a T-Distribution

Take the following example for how t-distributions are put to use in statistical analysis. First, remember that a confidence interval for the mean is a range of values, calculated from the data, meant to capture a “population” mean. This interval is m +- t*d/sqrt(n), where t is a critical value from the t-distribution.

For instance, a 95% confidence interval for the mean return of the Dow Jones Industrial Average (DJIA) in the 27 trading days prior to Sept. 11, 2001, is -0.33%, (+/- 2.055) * 1.07 / sqrt(27), giving a (persistent) mean return as some number between -0.75% and +0.09%. The number 2.055, the amount of standard errors to adjust by, is found from the t-distribution.

T-Distribution vs. Normal Distribution 

Normal distributions are used when the population distribution is assumed to be normal. The t-distribution is similar to the normal distribution, just with fatter tails. Both assume a normally distributed population. T-distributions thus have higher kurtosis than normal distributions. The probability of getting values very far from the mean is larger with a t-distribution than a normal distribution.

Limitations of Using a T-Distribution 

The t-distribution can skew exactness relative to the normal distribution. Its shortcoming only arises when there’s a need for perfect normality. The t-distribution should only be used when the population standard deviation is not known. If the population standard deviation is known and the sample size is large enough, the normal distribution should be used for better results.

The Bottom Line

The t-distribution is used in statistics to estimate the significance of population parameters for small sample sizes or unknown variations. Like the normal distribution, it is bell-shaped and symmetric. Unlike normal distributions, it has heavier tails, which result in a greater chance for extreme values.

What Is a Technical Indicator?

Technical indicators are heuristic or pattern-based signals produced by the price, volume, and/or open interest of a security or contract used by traders who follow technical analysis.

By analyzing historical data, technical analysts use indicators to predict future price movements. Examples of common technical indicators include the Relative Strength Index (RSI), Money Flow Index (MFI), stochastics, moving average convergence divergence (MACD), and Bollinger Bands®.

How Technical Indicators Work

Technical analysis is a trading discipline employed to evaluate investments and identify trading opportunities by analyzing statistical trends gathered from trading activity, such as price movement and volume. Unlike fundamental analysts, who attempt to evaluate a security’s intrinsic value based on financial or economic data, technical analysts focus on patterns of price movements, trading signals, and various other analytical charting tools to evaluate a security’s strength or weakness.

Technical analysis can be used on any security with historical trading data. This includes stocks, futures, commodities, fixed-income, currencies, and other securities. In this tutorial, we’ll usually analyze stocks in our examples, but keep in mind that these concepts can be applied to any type of security. In fact, technical analysis is far more prevalent in commodities and forex markets, where traders focus on short-term price movements.

Technical indicators, also known as “technicals,” are focused on historical trading data, such as price, volume, and open interest, rather than the fundamentals of a business, such as earnings, revenue, or profit margins. Technical indicators are commonly used by active traders, since they’re designed to analyze short-term price movements, but long-term investors may also use technical indicators to identify entry and exit points.

Types of Indicators

There are two basic types of technical indicators:

1. Overlays: Technical indicators that use the same scale as prices are plotted over the top of the prices on a stock chart. Examples include moving averages and Bollinger Bands®.
2. Oscillators: Technical indicators that oscillate between a local minimum and maximum are plotted above or below a price chart. Examples include the stochastic oscillator, MACD, or RSI.

Traders often use many different technical indicators when analyzing a security. With thousands of different options, traders must choose the indicators that work best for them and familiarize themselves with how they work. Traders may also combine technical indicators with more subjective forms of technical analysis, such as looking at chart patterns, to come up with trade ideas. Technical indicators can also be incorporated into automated trading systems, given their quantitative nature.

Example of Technical Indicators

The following chart shows some of the most common technical indicators, including moving averages, the RSI, and the MACD.

In this example, the 50- and 200-day moving averages are plotted over the top of the prices to show where the current price stands relative to its historical averages. The 50-day moving averages is higher than the 200-day moving average in this case, which suggests that the overall trend has been positive. The RSI above the chart shows the strength of the current trend—a neutral 49.07, in this case. The MACD below the chart shows how the two moving averages have converged or diverged—slightly bearish, in this case.