Jellybeans - Statistical Significance

Statistical Significance in Testing: Understanding the Concept of Confidence

In the world of research and data analysis, statistical significance plays a crucial role in determining the reliability and validity of experimental results. It provides us with a measure of confidence in the conclusions drawn from data. To ensure that our findings are not mere coincidences or random occurrences, we rely on the concept of confidence and statistical significance. In this blog post, we will delve into the meaning of statistical significance, explore the concept of confidence in testing, and provide a practical example to illustrate its importance.

Statistical Significance: A Definition

Statistical significance refers to the probability that an observed difference or relationship in a sample is not due to chance. It helps researchers determine if the results obtained from a sample can be generalized to the larger population from which the sample was drawn. In other words, statistical significance assesses the likelihood that the observed effects are real and not just random noise.

Understanding Confidence

Confidence is closely related to statistical significance and represents the degree of certainty we have in the results obtained from a sample. It is expressed as a percentage, typically ranging from 90% to 99%. For example, if we say we have 95% confidence in our results, it means we are 95% certain that the observed effects are not due to chance. For most experiments, 95% is a great guideline. You can raise or lower depending on the context of the data. For example, if you were running experiments on self driving car data, you would probably want that number much higher.

To grasp the concept of confidence better, let’s consider an example:

Example: A New Drug Treatment

Suppose a pharmaceutical company is testing a new drug treatment for a specific medical condition. They randomly select two groups of participants: Group A and Group B. Group A receives the new drug treatment, while Group B receives a placebo.

After a predetermined period, the researchers measure the reduction in symptoms for both groups. The collected data show that Group A experienced an average reduction in symptoms of 30%, while Group B only showed an average reduction of 10%.

Importance of Sample Size

In addition to the observed differences, the sample size plays a crucial role in determining statistical significance. Let’s explore two scenarios:

Scenario 1: Small Sample Size

In this scenario, the study had a small sample size, with only 20 participants in each group. After conducting a statistical analysis, the researchers calculate a p-value of 0.09 (If the p-value is 0.09, it means there is a 9% chance that the observed results occurred due to chance alone.). This p-value is larger than the commonly used significance level of 0.05 (If the p-value is 0.05, it means there is a 5% chance that the observed results occurred due to chance alone.). Therefore, the observed difference in symptom reduction between the two groups is not statistically significant. The researchers cannot confidently conclude that the new drug treatment is more effective than the placebo.

Scenario 2: Large Sample Size

Now, consider a scenario with a larger sample size. The study consists of 200 participants in each group. After analyzing the data, the researchers find a p-value of 0.001 (If the p-value is 0.001, it means there is a 0.1% chance (or 1 in 1000) that the observed results occurred due to chance alone.). In this case, the p-value is smaller than the significance level, indicating statistical significance. The researchers can confidently conclude that the observed difference in symptom reduction between the two groups is unlikely to be due to chance alone. They have a higher level of confidence in the effectiveness of the new drug treatment.

Statistical significance and confidence are fundamental concepts in testing and data analysis. They provide researchers with a framework for assessing the reliability of experimental findings. By understanding the concept of confidence and interpreting statistical significance correctly, we can make informed decisions and draw accurate conclusions from our data. In the example provided, we see how the sample size can impact the statistical significance of results. Adequate sample size is crucial to ensure reliable and meaningful findings. Remember, statistical significance is just one aspect of data analysis, and it is important to consider effect sizes, practical significance, and contextual factors for a comprehensive understanding of the results obtained.