Master the Hardest Parts of Statistics in a Snap
Quick Tips to Help You Understand Hypothesis Testing and Probability
No matter your career path, statistics can be an extremely intimidating subject. It makes most students nervous, insecure, and afraid to fail—and with good reason. Statistics uses Greek symbols and is built on concepts that are confusing for human brains to grasp. No wonder so many students struggle with this subject.
We chatted with our community of statistics students and tutors to understand the most frequently asked questions and biggest challenges students face in statistics today. Read on for the most common hiccups, and leave with a few pro tips that you can put to use, well, stat!
Many students wonder, “Why can’t I just skip statistics?”
Oftentimes, stats can feel inescapable. That’s because people pursuing all kinds of careers have to pass a statistics course to achieve their larger professional goals. (Yes, even if they think they won’t ever use stats in their future jobs.)
No matter what career you’re pursuing, if you’re struggling with statistics you’re not alone. Here are the career paths of 235 students we surveyed who recently overcame their statistics challenges:
70% of these students struggled with the same two concepts
Interviews with top statistics tutors on Wyzant confirm that students across degrees and career paths have similar struggles with statistics.
Interestingly, 45% of the students we surveyed said “I’m not a math person,” which only adds to the anxiety and mystery around stats. Even more students feel overwhelmed by all the formulas and procedures, which they think they need to remember.
But here’s some good news: You don’t need to memorize the formulas or procedures in statistics. You just need to know which ones to use and when.
We sat down with professional statistics tutors to walk through the two biggest stats challenges that students face today—and got some very useful tips along the way.
Challenge #1: Hypothesis Testing
Meet Mica. Mica has a Masters Degree in statistics, has worked as a statistician at The Gallup Organization, and has spent thousands of hours tutoring students struggling with statistics.
First off, look at this formula sheet. There are A LOT of formulas, yes, but you’re not supposed to memorize them. I haven’t memorized them, and I teach this stuff.
See how the formulas are grouped together in different boxes?
It’s important to read the word problem carefully to understand which recipes or formulas to use. But once you understand what the word problem is trying to solve, all you need to do is pick out the right statistic formula and follow the steps of the recipe to get the answer.
Here are the basic steps to a hypothesis test:
1. Set up the null & alternative hypothesis
Translation = Define what question the researcher is asking (alternative hypothesis) and what is the status quo (null hypothesis)
2. Decide the significance level you will use to reject or fail to reject the null hypothesis (i.e. 10%, 5%, 1%)
Translation = How confident do you need to be in the results of your test? 90% confident? 95% confident? 99% confident?
3. Calculate your test statistic (z-statistic, t-statistic, etc.)
Translation = Calculate how different your test result is from what normally happens.
4. Find the critical value or P-value
Translation = If you repeated the experiment 100 times, how often would you come to a different conclusion?
5. Reject or fail to reject the null hypothesis and interpret the results
Translation = Are you confident enough in the result of your test to say it’s not just due to random chance (reject the null hypothesis)?
Don’t let hypothesis testing scare you. First, take a few deep breaths. Now, let’s look at the five steps in greater depth. I like to think of hypothesis testing the same way a baker thinks of a recipe.
Steps #1, 2, 4, and 5 don’t change. In step #1, you gather all of the ingredients you need. In step #2, you preheat the oven. In step #4, you bake your dish in the oven. And in step #5, you remove your creation from the oven and serve. The only step that changes is #3, which addresses what ingredients you will use, and how to combine them. Again, you don’t have to memorize the formulas, and a computer or calculator can do the math for you. You just have to pick which formulas (or recipe) to use based on what the problem tells you (what ingredients you have).
So, what kind of information will the problem give you to help you choose the right recipe or formula to use?
First, look for info in the problem about the number of groups, and how to compare them. For example,
If there is only one group, then you use a one-sample t-test or z-test (Use a z-test if you know the standard deviation of the population and your sample size is greater than 30. Otherwise use a t-test.)
If you’re comparing the same group with a before-and-after test, then you will want the paired sample t-test
If there are two separate groups, like a test and control group, then you will want a two sample t-test or z-test
If you are looking at the effect of three or more groups, then you might use a one-way ANOVA test
Second, determine which statistic the problem is asking you about. Is it means or proportions? Use this information to select the right formula for calculating your z-score or t-score.
Read the problem carefully to understand how many groups and what statistic you’re dealing with, and then pick the right formula (or recipe). That’s it!
For more helpful tips, check out this guide on hypothesis testing.
Challenge #2: Probability
Meet Brian. Brian has a PhD from the University of Illinois at Chicago in Game Theory, Probability, and Statistics. He currently teaches university-level statistics courses and has experience tutoring hundreds of students 1-to-1 who are struggling to understand statistics.
I’ve created a clever way to help students develop intuition about the normal distribution. I call it “the pixel normal distribution,” and it will visually help you understand probability and the area under the curve.
Take a look at the graphic below.
This 100-block pixel graphic approximates the shape of a normal distribution, but every block counts for 1% probability. If you simply count the blocks, you’ll get a sense of your probability in a certain region.
Typically, when students are introduced to the normal distribution, they’re given a curve and told probability is the area under the curve. But this is still confusing. If you can look at the distribution and say each of these squares is equal to 1% probability, you can just count the squares to develop good intuition about what the normal distribution is and what it means.
For more probability tips, check out our guide on statistics and probability.
Still feel like you’re struggling?
That’s okay. Statistics is a complicated subject and sometimes a little too easy to misunderstand. Know that you’re not alone, and that there are plenty of resources to help you along your path. Here are a few of our favorite websites packed with helpful statistics tips.