The raw results of the statistical analysis

Let’s imagine a study that looks at how sleep affects test scores. Picture researchers collecting information from 100 students, measuring how many hours each student slept before a test and their scores. After studying the data, the researchers found a strong connection between sleep and test scores.

If we don’t understand the basic outcomes of the statistical analysis, we might think that “more sleep guarantees better grades.” But that might not be the whole story!

When we dig deeper into the results, we realize that the connection between sleep and test scores is actually quite weak. It means that while there is a relationship, it’s not a very strong one. We also find that there’s some uncertainty in the results. This means that other things, like how well we study, how motivated we are, or how nervous we feel during tests, can also affect our scores.

If we don’t know these basic outcomes, we might wrongly think that sleep is the only thing that matters for doing well in school. We might forget about the other important factors.

Understanding the raw results of the statistical analysis helps us avoid making quick judgments.


What to Consider as You Think About Your Results
  • Make sure you’re reading it right: Just like reading a book, we need to read the numbers correctly. A statistical test doesn’t tell us if a result is really important. It only gives us an idea of the chance that the result happened randomly. So, we need to be careful and not jump to conclusions too quickly.
  • Don’t be tricked into wrong ideas: Sometimes, we might only focus on one number called the p-value. It tells us if the result is random or not. But that’s not the whole story! We need to look at other important details, too, like the effect size. This tells us how big the difference or change really is. We also need to consider the confidence interval, which tells us how certain we can be in the results.
  • Avoid jumping to conclusions: We should be cautious and not assume our results are always true. There’s always a chance that they happened randomly. Especially if we didn’t have many samples or our test wasn’t right. So, let’s take a step back and carefully consider the basic outcomes before drawing conclusions. Knowing the basic outcomes can stop you from guessing what they mean too quickly.
  • Help others to repeat your study: Imagine you make an amazing discovery and want others to learn from it. If other researchers want to replicate your study, they need to understand the raw outputs of your statistical tests. If your conclusions don’t match the raw data, people might not believe in your study. So, it’s important to share the basic outcomes to help others understand and trust your findings.
  • Don’t fall into the trap of multiple testing: Sometimes, we get excited and want to test many things at once. However, doing a lot of tests increases the chance of finding a significant result just by luck. To avoid this trap, we need to know the basic outcomes and make corrections to control the error rate.


Steps You Should Take to Understand the Basic Outcomes of a Statistical Analysis or Hypothesis Test
  1. Make sense of the test statistic: The test statistic, like the t-value, F-value, or chi-square value, gives us a clue about the size of the effect we are studying. It tells us how many standard deviations it is from the null hypothesis, which is the idea that there is no effect.  This means the larger the test statistic, the more likely it is that the results are not due to random chance.  To make sense of this number, we need to understand our specific test.
    • For example, suppose the t-value exceeds the critical t-value or falls outside the range of the critical t-values. In that case, it suggests that the observed difference is unlikely to have occurred by chance alone, and we reject the null hypothesis.
  2. Make sense of the p-value: The p-value tells us the chance that we would see a test statistic as extreme as the one we got if the null hypothesis were true. It’s like a measure of surprise. Remember, it doesn’t tell us the chance that the null hypothesis is true, but rather the chance of seeing such an extreme result if it were true.
  3. Make sense of confidence intervals: Confidence intervals give us an estimated range of values where the unknown true value for everyone in the population could be. It’s calculated based on the data we have. So, instead of just focusing on single estimates, we should consider the variability and the range of possible values.
  4. Visually check the results: Sometimes, seeing is believing! Visualizing our data and results can help us understand the story our data is telling. We can use various charts, plots, and infographics to present our statistical results in a clear and engaging way.


Best Practices for Understanding the Basic Outcomes of a Statistical Analysis

Remember, before we draw conclusions and make decisions based on statistics, let’s understand the basic outcomes of our analysis. It’s like solving a puzzle, where each number and result has a story to tell. By being curious, careful, and thorough, we can unlock the secrets hidden within the data and make informed decisions that shape our understanding of the world. Here are some tips for understanding your outcomes:

  • Make sure to interpret p-values correctly: Many people get p-values wrong, thinking they tell us the chance that the null hypothesis is true. But that’s not the case! If the null hypothesis is true, p-values should be understood as the chance of seeing a result as extreme as the one in our data. So, let’s interpret p-values carefully and avoid misconceptions.
  • Don’t forget to think about confidence intervals: Confidence intervals utilize population estimates to provide a range of values within which the true population parameter is likely to fall. Translation: Confidence intervals give us a range where we can expect the true value for everyone in the population to be, with a certain level of confidence. It’s important not to focus only on single estimates but to consider the variability and the range of possible values.
  • Double-check your results: Just like proofreading an important essay, we need to double-check our statistical results. We can repeat the tests, use different statistical software, or ask a friend or expert to review our work. This helps us ensure the accuracy and reliability of our findings.



Can Music Really Make Someone Happy?

Meet Alex, a high school student with a deep love for music. Alex has always wondered about the connection between music and emotions. Does the type of music we listen to affect how we feel? To find answers, Alex decides to embark on a statistical analysis adventure.

Alex starts by collecting data from a group of classmates. The data includes information about their favorite genres of music and their corresponding emotions. With the data in hand, Alex begins the journey of analyzing the raw results.

Upon diving into the numbers, Alex discovers something fascinating. There is a clear pattern in the data. People who enjoy upbeat and energetic music tend to feel more positive emotions, like happiness and excitement. On the other hand, those who prefer slower, more soothing music often experience calmness and relaxation.

However, Alex knows that understanding the basic outcomes of the statistical analysis is crucial before jumping to conclusions. It’s time to dig deeper.

As Alex examines the raw results further, a new insight emerges. While there is a correlation between music and emotions, it’s important to remember that correlation does not imply causation. In other words, just because there is a connection between the type of music and emotions, it doesn’t mean that music directly causes those emotions.

To gain a better understanding, Alex considers other factors that could be influencing emotions. Alex takes into account individual preferences, personal experiences, and even external factors like the environment. It becomes clear that emotions are complex and can be influenced by a variety of factors beyond just music.

By interpreting the raw results with caution, Alex avoids making hasty generalizations. The analysis helps Alex see that while there is a relationship between music and emotions, it is part of a larger picture. Factors like personal taste and individual experiences contribute to how music affects our emotional state.

Armed with this knowledge, Alex can appreciate the power of music in evoking emotions while understanding that emotions are multi-faceted and influenced by various factors. Whether it’s a lively tune that brings joy or a soothing melody that promotes relaxation, music is a powerful tool that can enhance our emotional experiences.