Statistical significance is important because it gives you confidence in your analysis and its resulting insights. Statistical significance is often calculated with statistical hypothesis testing, which tests the validity of a hypothesis by figuring out the probability that your results have happened by chance. The result of a hypothesis test allows us to see whether this assumption holds under scrutiny or not. The testing part of hypothesis tests allows us to determine which theory, the null or alternative, is better supported by data.
But, before we get to the Z-test, it is important for us to visit some other statistical concepts the Z-test relies on. Normal distribution is used to represent how data is distributed and is primarily defined by:. A normal distribution curve Image source — Wikipedia. A normal distribution curve is used to assess the location of a data point in terms of the standard deviation and mean.
This allows you to determine how anomalous a data point is based on how many standard deviations it is from the statistical mean. The properties of a normal distribution mean that:. If we have a normal distribution for a data set, we can locate any data point by the number of standard deviations it is away from the mean.
If an app called MixTunes has downloads, we can say that it is 2 standard deviations above the mean and is in the top 2.
In statistics, the distance between a data point and the mean of the data set is assessed as a Z-score. The Z-score also known as the standard score is the number of standard deviations by which a data point is distanced from the mean.
In the example we discussed above, MixTunes would have a Z-score of 2 since the mean is downloads and the standard deviation is downloads. Assuming a normal distribution lets us determine how meaningful the result you observe in an analysis is, the higher the magnitude of the Z-score either positive or negative , the more unlikely the result is to happen by chance, and the more likely it is to be meaningful.
To quantify just how meaningful the result of your analysis is, we use one more concept. In studies where a sample of an overall population is considered like surveys and polls , the Z-value formula is slightly changed to account for the fact that each sample can vary from the overall population, and thus have a standard deviation from the overall distribution of all samples.
The final concept we need to use the Z-test is that of P-values. We call that degree of confidence our confidence level , which demonstrates how sure we are that our data was not skewed by random chance. More specifically, the confidence level is the likelihood that an interval will contain values for the parameter we're testing. This info probably doesn't make a whole lot of sense if you're not already acquainted with the terms involved in calculating statistical significance, so let's take a look at what it means in practice.
Say, for example, that we want to determine the average typing speed of year-olds in America. We'll confirm our results using the second method, our confidence interval, as it's the simplest to explain quickly. First, we'll need to set our p-value , which tells us the probability of our results being at least as extreme as they were in our sample data if our null hypothesis a statement that there is no difference between tested information , such as that all year-old students type at the same speed is true.
A typical p-value is 5 percent, or 0. For our experiment, 5 percent is fine. If our p-value is 5 percent, our confidence level is 95 percent—it's always the inverse of your p-value. Our confidence level expresses how sure we are that, if we were to repeat our experiment with another sample, we would get the same averages— it is not a representation of the likelihood that the entire population will fall within this range. Testing the typing speed of every year-old in America is unfeasible, so we'll take a sample— year-olds from a variety of places and backgrounds within the US.
Once we average all that data, we determine the average typing speed of our sample is 45 words per minute, with a standard deviation of five words per minute. That's our confidence interval —a range of numbers we can be confident contain our true value, in this case the real average of the typing speed of year-old Americans.
More importantly for our purposes, if your confidence interval doesn't include the null hypothesis, your result is statistically significant. Since our results demonstrate that not all year-olds type the same speed, our results are significant. One reason you might set your confidence rating lower is if you are concerned about sampling errors.
A sampling error , which is a common cause for skewed data, is what happens when your study is based on flawed data. For example, if you polled a group of people at McDonald's about their favorite foods, you'd probably get a good amount of people saying hamburgers. If you polled the people at a vegan restaurant, you'd be unlikely to get the same results, so if your conclusion from the first study is that most peoples' favorite food is hamburgers, you're relying on a sampling error.
It's important to remember that statistical significance is not necessarily a guarantee that something is objectively true. Statistical significance can be strong or weak, and researchers can factor in bias or variances to figure out how valid the conclusion is.
Any rigorous study will have numerous phases of testing—one person chewing rocks and not getting cancer is not a rigorous study. Essentially, statistical significance tells you that your hypothesis has basis and is worth studying further. For example, say you have a suspicion that a quarter might be weighted unevenly. If you flip it times and get 75 heads and 25 tails, that might suggest that the coin is rigged. That result, which deviates from expectations by over 5 percent, is statistically significant.
The results are statistically significant in that there is a clear tendency to flip heads over tails, but that itself is not an indication that the coin is flawed. Statistical significance is important in a variety of fields— any time you need to test whether something is effective, statistical significance plays a role.
This can be very simple, like determining whether the dice produced for a tabletop role-playing game are well-balanced, or it can be very complex, like determining whether a new medicine that sometimes causes an unpleasant side effect is still worth releasing.
Statistical significance is also frequently used in business to determine whether one thing is more effective than another. In school, you're most likely to learn about statistical significance in a science or statistics context, but it can be applied in a great number of fields.
Any time you need to determine whether something is demonstrably true or just up to chance, you can use statistical significance! Calculating statistical significance is complex—most people use calculators rather than try to solve equations by hand. Z-test calculators and t-test calculators are two ways you can drastically slim down the amount of work you have to do. However, learning how to calculate statistical significance by hand is a great way to ensure you really understand how each piece works.
Let's go through the process step by step! To set up calculating statistical significance, first designate your null hypothesis, or H 0. Your null hypothesis should state that there is no difference between your data sets. For example, let's say we're testing the effectiveness of a fertilizer by taking half of a group of 20 plants and treating half of them with fertilizer.
Our null hypothesis will be something like, "This fertilizer will have no effect on the plant's growth. Next, you need an alternative hypothesis, H a.
Your alternative hypothesis is generally the opposite of your null hypothesis , so in this case it would be something like, "This fertilizer will cause the plants who get treated with it to grow faster. The alpha is the probability of rejecting a null hypothesis when that hypothesis is true. In the case of our fertilizer example, the alpha is the probability of concluding that the fertilizer does make plants treated with it grow more when the fertilizer does not actually have an effect.
An alpha of 0. For our fertilizer experiment, a 0. Again, your alpha can be changed depending on the sensitivity of the experiment, but most will use 0. RStudio is a tool created for data science and statistical computing.
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