Okay, we've all heard the terms 'parametric' and 'non-parametric tests,' but what are they exactly? You can think of them like superheroes, each with its strengths and weaknesses!

• Parametric tests are like the Superman of tests - powerful, with the ability to detect differences even when they are hiding. It's like Superman's X-ray vision! They use interval or ratio-level measurements and make assumptions about the population parameters (like a normal distribution). This is pretty neat, but like Superman with his kryptonite, they do have a weakness: they rely heavily on the assumption of normality in data distribution, especially for small sample sizes.

• Non-parametric tests, on the other hand, are more like Batman - they don't have the same superpower level as Superman, but they're really good at handling "dirty" data, or data that doesn't meet the assumptions of parametric tests. They use ordinal-level measurements, hence don't assume a normal distribution. However, they might miss some hidden differences because they are less sensitive.

Remember though, they are both heroes in their own way! The choice between them depends on the nature of your data and the assumptions you can make.

Now, let's move to the 'Unrelated t-test.' Sounds complicated, right? Nope, it's just like a friendly game between two separate soccer teams. Each team has its own set of players (samples) and the t-test is the referee, checking if there's a significant difference in their skills (means). Let's break down its superpowers (assumptions)

• Interval or Ratio-level Measurement: It's like knowing the exact distance each player can kick the ball.
• Independent Measures Design: Two different soccer teams playing, not the same team playing against itself!
• Normal Distribution: Just like expecting most of the players to be moderately fit, with very few super unfit or super fit players.
• Homogeneity of Variances: Similar fitness level across both teams.

Imagine you have two teams, Team "Quiet" and Team "Noisy," and you predict Team "Quiet" will perform better. You check your t-test referee's decision against the "critical values table," like comparing the actual game result to the predicted result. If the t-test statistic is beyond the critical value, you've got a winner! You reject the null hypothesis (that both teams perform the same) and accept the experimental hypothesis (that Team "Quiet" performs better).