8 Ways to Improve Your Brain Power

To increase power:

1. Increase alpha.
2. Conduct a one-tailed test.
3. Increase the effect size.
4. Decrease random error.
5. Increase sample size.

What three factors can be decreased to increase power? Population standard deviation, standard error, beta error.

1. Exercise. We all know that we should be getting regular exercise.
2. Drink coffee. Many people start their days with a cup of coffee, and it turns out this ritual could actually benefit your cognitive functions in the short term.
3. Get some sunlight.
4. Build strong connections.
5. Meditate.
6. Sleep well.
7. Eat well.
8. Play Tetris.

Foods linked to better brainpower

• Green, leafy vegetables. Leafy greens such as kale, spinach, collards, and broccoli are rich in brain-healthy nutrients like vitamin K, lutein, folate, and beta carotene.
• Fatty fish.
• Berries.
• Tea and coffee.
• Walnuts.

As the sample size gets larger, the z value increases therefore we will more likely to reject the null hypothesis; less likely to fail to reject the null hypothesis, thus the power of the test increases.

If the null hypothesis is true, then the probability of making a Type I error is equal to the significance level of the test. To decrease the probability of a Type I error, decrease the significance level. Changing the sample size has no effect on the probability of a Type I error.

To increase the power of your study, use more potent interventions that have bigger effects; increase the size of the sample/subjects; reduce measurement error (use highly valid outcome measures); and relax the α level, if making a type I error is highly unlikely.

Effect size formulas exist for differences in completion rates, correlations, and ANOVAs. They are a key ingredient when thinking about finding the right sample size. When sample sizes are small (usually below 20) the effect size estimate is actually a bit overstated (called biased).

In statistics analysis, the effect size is usually measured in three ways: (1) standardized mean difference, (2) odd ratio, (3) correlation coefficient. The effect size of the population can be known by dividing the two population mean differences by their standard deviation.

The statistical power of a significance test depends on: • The sample size (n): when n increases, the power increases; • The significance level (α): when α increases, the power increases; • The effect size (explained below): when the effect size increases, the power increases.

As our sample size increases, the confidence in our estimate increases, our uncertainty decreases and we have greater precision.

Cohen suggested that d = 0.2 be considered a ‘small’ effect size, 0.5 represents a ‘medium’ effect size and 0.8 a ‘large’ effect size. This means that if the difference between two groups’ means is less than 0.2 standard deviations, the difference is negligible, even if it is statistically significant.

Effect size tells you how meaningful the relationship between variables or the difference between groups is. It indicates the practical significance of a research outcome. A large effect size means that a research finding has practical significance, while a small effect size indicates limited practical applications.

Effect size is a simple way of quantifying the difference between two groups that has many advantages over the use of tests of statistical significance alone. Effect size emphasises the size of the difference rather than confounding this with sample size. A number of alternative measures of effect size are described.

Unlike correlation coefficients, both Cohen’s d and beta can be greater than one. So while you can compare them to each other, you can’t just look at one and tell right away what is big or small. You’re just looking at the effect of the independent variable in terms of standard deviations.

Values that do not reach significance are worthless and should not be reported. The reporting of effect sizes is likely worse in many cases. Significance is obtained by using the standard error, instead of the standard deviation.