p-value

p-value for the layman

Statistics can often feel like a labyrinth of complex numbers and jargon. In the world of statistics, p-values are your compass. While the concept may seem a bit abstract at first, p-values are like a traffic light for your scientific discoveries, guiding you to proceed with caution or giving you the green light to embrace a new understanding of the world.

What is a p-value?

At its core, a p-value is a number that helps us determine the significance of an observation or result in statistical analysis. Imagine you've conducted an experiment or a survey, and you want to know if your findings are meaningful or just a result of chance. The p-value is your guide.

The Role of Probability

To grasp p-values, you need to understand the concept of probability. Think of it as a measure of how likely something is to happen. In statistics, we often want to know the probability of observing certain data if there's no real effect or difference. This is where p-values come into play.

Hypotheses: The Foundation

In any scientific study, you start with two hypotheses: the null hypothesis (H0) and the alternative hypothesis (H1). The null hypothesis represents the idea that there's no significant effect or difference, while the alternative hypothesis suggests the opposite – that there is a significant effect or difference.


The Experiment and the Data

You gather your data, conduct your analysis, and calculate a test statistic, which quantifies the difference between your observed data and what you would expect under the null hypothesis. This test statistic follows a particular distribution, like the normal distribution for many common statistical tests.

The P-Value's Revelation

Here's the moment of truth: the p-value tells you the probability of obtaining a test statistic as extreme as, or more extreme than, the one you calculated if the null hypothesis is true. In simpler terms, it answers the question: "How likely is it that my observed results are just due to random chance?"

Interpreting P-Values

Now, the key interpretation comes into play. If your p-value is small, typically less than 0.05 (but it can vary depending on the field), it suggests that your observed results are unlikely to have occurred by chance alone. This is your green light to reject the null hypothesis and accept that you've found something significant.

Conversely, if your p-value is large (greater than 0.05), it indicates that your observed results are quite likely to be explained by random chance, and you should stick with the null hypothesis.

It's Not Absolute Proof

One crucial thing to understand is that p-values don't provide absolute proof or disproof. They offer a level of evidence, but they can't tell you the size of an effect or whether it's practically meaningful. They merely guide you in determining if your results are statistically significant.

Low Crohbach's Alpha

[Concepts in Research Statistical Analysis] 

In psychological and social sciences research, Cronbach's alpha is often used as a measure of internal consistency, which reflects how closely related a set of items are as a group. 

The alpha coefficient ranges in value from 0 to 1 and can be used to describe the reliability of factors extracted from dichotomous (that is, questions with two possible answers) and/or multi-point formatted questionnaires or scales. 

A high value of alpha (usually 0.7 or above) is taken as an indication that the items measure an underlying (or latent) construct. In other words, it indicates that the scale or test has good internal consistency and that the items within the scale reliably measure the same construct. 

If the Cronbach's alpha is low (below 0.7, and especially below 0.6), it suggests that the items in the scale may not be measuring the same construct; they could be disparate and not well related. For instance, if you have a low alpha for the specific subscale, it suggests that the questions intended to measure that subscale may not be working well together to accurately and reliably assess extraversion in your sample. 

However, a low alpha doesn't necessarily mean your measure is "bad." It could be that your measure is multidimensional (i.e., measuring multiple factors) rather than unidimensional. In addition, alpha is sensitive to the number of items in a scale; scales with fewer items can result in a lower alpha. Further, sometimes scales designed to cover a broad concept may naturally have a lower alpha. 

ie, a low alpha can be an indicator to check your scale or test more thoroughly to understand whether all items are appropriate for your construct and your population. It may also signal the need for additional scales or tests to ensure you're capturing all aspects of a construct.