Maths Statistics T-Test Correlations Anova p-test statical significance

Priekš aprēķiniem ieteicams izmantot software JASP - visi algos implementēti, bet var izmantot arī python libs SciPy, Statsmodels, and Pingouin

Statistical signficance

https://pro.arcgis.com/en/pro-app/latest/tool-reference/spatial-statistics/what-is-a-z-score-what-is-a-p-value.htm

https://stats.stackexchange.com/questions/240453/statistical-significance-of-multiple-classifiers-by-using-p-value

The threshold below which we reject the null hypothesis is called the significance level, often denoted by alpha (α). This is commonly set at 0.05, meaning that there is a 5% chance we will reject the null hypothesis when it is true.

The choice between a one-tailed and a two-tailed test depends on the nature of the research question.

In a one-tailed test, you're testing for the possibility of the relationship in one direction and completely disregarding the possibility of a relationship in the other direction. The p-value in a one-tailed test is the area under the curve of the distribution to one side (the side specified in your hypothesis).
In a two-tailed test, you're testing for the possibility of the relationship in both directions. The p-value in a two-tailed test is the total area under the curve of the distribution to both sides of your observed statistic.

That being said, the threshold for statistical significance (often set at 0.05) is the same for both one-tailed and two-tailed tests. What changes between the two is how the p-value is calculated and where that threshold is applied in the distribution. In a two-tailed test, the 0.05 threshold is split into two, with 0.025 in each tail of the distribution. In a one-tailed test, the full 0.05 is in the one tail that you're testing for.

If P(T<=t) is small (typically, less than 0.05), then it suggests that the difference in means you observed is unlikely to have occurred by chance, and you might reject the null hypothesis and conclude that there is a significant difference between the groups.

In statistics, "df" stands for "degrees of freedom." It's a fundamental concept that refers to the number of values in a calculation that are free to vary.

Z-Score

Karam eksperimentam noteikt statistical significance

https://www.simplypsychology.org/z-score.html

https://www.makeuseof.com/how-to-calculate-z-score-excel/

t-test/p-test

Testēt eksperemntu grupu atšķirības (2 grupas)

https://www.indeed.com/career-advice/career-development/how-to-calculate-p-value-in-excel

https://www.scribbr.com/statistics/statistical-tests/

Correlation between 2 scalar variables series

https://web.pdx.edu/~newsomj/uvclass/ho_correlation%20t%20phi.pdf

statistical significance between 2 groups (paired - no inter-dependence, unpaired - inter-dependence exists)

A t-test is a type of inferential statistic used to determine if there is a significant difference between the means of two groups, which may be related in certain features.

https://www.investopedia.com/terms/t/t-test.asp

One-sample, two-sample, or paired t-test?

If the groups come from a single population (e.g. measuring before and after an experimental treatment), perform a paired t-test.
If the groups come from two different populations (e.g. two different species, or people from two separate cities), perform a two-sample t-test (a.k.a. independent t-test).
If there is one group being compared against a standard value (e.g. comparing the acidity of a liquid to a neutral pH of 7), perform a one-sample t-test.

One-tailed or two-tailed t-test?

If you only care whether the two populations are different from one another, perform a two-tailed t-test.
If you want to know whether one population mean is greater than or less than the other, perform a one-tailed t-test.

https://www.scribbr.com/statistics/t-test/

ANOVA uses the F-test The Pr(>F) column is the p-value of the F-statistic.

Use a one-way ANOVA when you have collected data about one categorical independent variable and one quantitative dependent variable. The independent variable should have at least three levels (i.e. at least three different groups or categories).

https://www.scribbr.com/statistics/one-way-anova/

p-value https://www.scribbr.com/statistics/p-value/

Performing a One-Sample T-Test in Excel is quite straightforward. Here are the steps:

Organize your data: The first step is to have your data in Excel. Suppose you have a column of data representing a sample for which you want to conduct a One-Sample T-Test. Let's say that your data is in cells A2 to A101, and the test value (the population mean you're comparing against) is 5.
Use the T.TEST function: Excel has a function called T.TEST that conducts a t-test. To perform a One-Sample T-Test, you'll want to use this function.
Here's how you might do it:
=T.TEST(A2:A101, B2:B101, 1, 1)
In this formula:
- A2:A101 represents the range of your data.
- B2:B101 is a range of cells with the same number of rows as your data, but each cell contains the population mean you're comparing against (in this case, 5). In other words, you should fill cells B2 to B101 with the value 5.
- The first '1' is the type of t-test you want to conduct. '1' is for a one-tailed test, and '2' is for a two-tailed test. Choose based on your research question.
- The second '1' is for the type of variance. '1' is for paired data or equal variances, and '2' is for unequal variances. In a One-Sample T-Test, you use '1'.
Interpret the result: The T.TEST function will return the p-value for the t-test. If this p-value is less than your chosen significance level (often 0.05), then you can reject the null hypothesis and conclude that the mean of your sample is significantly different from the test value.