Correlation and regression and parametric and non parametric distributions

Parametric distibution

Assumes data follows a specific pattern usually normal distribution with parameters like mean and variance

Parametric distribution

Normal bell shaped, t distribution, f distribution, binomial, poisson, exponential

Parametric distribution

When used, data is continuous, normally distributed, large sample size, meets assumptions, linearity, equal variance, independence

Non parametric distribution

Does not assume any specific distribution, also called distribution free

Non parametric distribution

Works with ordinal or nominal data, handles skewed or small datasets, uses ranks instead of raw values

Non parametric distribution

Spearman correlation, manny whitney u, kruskal wallis, wilcoxon test

Parametric distribution

Strict assumptions, interval or ratio data, large sample size, higher power, used when data is normal

Non parametric distribution

Flexible assumptions, ordinal or norminal data, small sample size, lower power, used when data is skewed

Correlation

Is a statistical measure that shows the relationship between two variables

Correlation

Measures how variables change together, describes relationships but does not indicate cause and effect

Purpose of correlation

Identifies patterns and relationships between variables, measures the strength and direction of relationships, helps in prediction and decision making, simplifies data by identifying important variables, useful in fields like finance, healthcare, and research

Positive correlation

Both variables move in the same direction, when one increases, the other also increases, when one decreases, the other also decreases

Negative correlation

Variables move in opposite directions, when one variable increases, the other decreases, inverse correlation

Zero correlation

No relationship exists between the variables, changes in one variable do not affect the other

Strong correlation

Means the variables have a very close relationship, where changes in one consistently associated with changes in the other

Moderate correlation

Indicates a noticeable relationship, but it is not perfectly consistent and may have some variation

Weak correlation

Shows little to no clear relationship, meaning changes in one variable do not strongly predict changes in the other

Pearson correlation coefficient

Is a statistical measure of the linesr relationship between two variables, it is a descriptive statistic that summarizes data characteristics

Perfect positive relationship

+1 correlation

Perfect negative relationship

-1 correlation

No relationship

0 correlation

Pearson correlation coefficient

Used for continuous data, applied when both variables are measured on a continuous scale, best used when the relationship between variables is linear

Pearson correlation

Assumes that the data are normally distributed, it also assumes a linesr relationship between the two variables, this means the data should follow a bell shaped pattern and change consistently in one direction, if these assumptions are not met, the results may be inaccurate

Spearman rank correlation

Measures the strength and direction of a linear relationship between two variables, commonly used for continuous data such as height, weight, or test scores, assumes normal distribution and a linear relationship between variables

Kendall’s Tau

Nonparametric measure of association between two ranked variables, more accurate when there are many tied ranks, commonly used for small sample sizes

Regression

Is a statistical method used to examine relationships between variables

Regression

Helps determine how one variable can predict another

Regression

Used to identify patterns and trends for analysis and decision-making

Regression

Explains how one variable affects another and is used for prediction

Purpose of regression analysis

Understands relationships between variable, predicts future outcomes, identifies variables that strongly influence an outcome

Regression

Estimates the value of one variable based on another variable, useful for forecasting and decision-making

Regression

Measures how an independent variable affects a dependent variable, shows whether the effect is positive, negative, or no effect, helps determine the strength and direction of the effect between variables

Simple linear regression

Is used when there is one independent variable and one dependent variable

Simple linear regression

The method assumes a straight-line relationship, meaning as the independent variable changes, the dependent variable changes at a constant rate

Multiple regression

Involves two or more independent variables affecting a single dependent variable

Multiple regression

This type helps measure how several factors together influence an outcome and can show which variables have the strongest impact

Logistic regression

It is when the dependent variable is categorical pass or fail, estimates the probability of a certain

outcome

Logistic regression

Used when the dependent variable is categorical, such as yes or no or passor fail outcomes, instead of predicting a numeric value, it estimates the probability of an event occurring

Linear regression

Predicts continuous values, uses best-fit line, solves regression problems

Logistic regression

Predicts categorical classes, uses sigmoid s curve, solves classification problems

Non linear regression

Is a statistical method that models complex, curved relationships between a dependent variable and one or more independent variables

Non linear regression

Uses flexible curves such as exponential, logarithmic, or logistic functions to fit data that does not follow a linear pattern

Parametric distribution

Assume data follows a specific probability distribution, described using parameters such as mean and variance

Parametric distribution

Used for prediction, hypothesis testing, and statistical analysis, accurate only when the data fits the assumed distribution

Normal distribution

Also called the Gaussian or bell-shaped distribution, symmetrical around the mean, defined by mean and standard deviation, commonly used for heights, test scores, and measurement errors

t distribution

Similar to the normal distribution but with wider tails, used for small sample sizes usually below 30

t distribution

Defined by degrees of freedom, commonly used in t-tests for comparing means

F distribution

Positive and right-skewed distribution, based on the ratio of two variances, defined by two degrees of freedom, commonly used in anova to compare group means

Parametric tests

Use when data is continuous, interval or ratio scale, data should be approximately normally distributed bell-shaped, variances of groups should be equal homoscedasticity, observations must be independent, best used with moderate to large sample sizes

Non parametric distribution

Methods do not assume a normal distribution of data, also called distribution-free methods, analyze data using ranks, order, or categories instead of means and standard deviation

Non parametric tests

Does not require normality, can handle skewed data and outliers, suitable for small sample sizes, can be used for ordinal and nominal data

Spearman correlation

Measures the relationship between two ranked variables, used for ordinal or non-normally distributed data

Mann-Whitney U test

Compares two independent groups, non-parametric alternative to the independent samples t-test, uses ranks instead of means

Kruskal-Wallis test

Compares three or more independent groups, non-parametric alternative to one-way anova, determines if significant differences exist among groups

Wilcoxon test

Compares two related samples or repeated measurements, non-parametric alternative to the paired samples t-test, often used for before-and-after measurements

Parametric assumptions

Requires the data to follow certain conditions such as normal distribution, equal variance, and independence of observations, these assumptions allow more accurate and powerful statistical conclusions

Non parametric assumptions

Does not require strict assumptions about the distribution of data, it can be used even when data are skewed, not normally distributed, or contain outliers

Parametric type of data

Used for interval and ratio data, where numerical values have equal intervals, these data allow computation of mean and standard deviation

Non parametric type of data

Used for ordinal and nominal data, where values represent categories or rankings

Parametric sample size

Works best with larger sample sizes because the assumption of normality becomes more reliable, larger samples improve accuracy of results

Non parametric sample size

Can be used with small sample sizes since it does not rely heavily on distribution assumptions, it is useful when there are few participants

Parametric statistical power

Has higher statistical power, meaning it is more likely to detect a true difference or relationship if one exists, this makes parametric tests more sensitive

Non parametric statistical power

Has lower statistical power, meaning it may fail to detect small differences, it is safer when assumptions for parametric tests are violated

One sample t test

Compares one group with a known standard or population mean

Independent samples t test

Compares the means of two independent groups

Paired samples t test

Compares the mean of the same group before and after

One-Way ANOVA

Compares the means of three or more independent groups

Pearson r

Measures the relationship between two variables

Mann-Whitney U test

Alternative to independent t-test, compares 2 independent groups, it calculates a U statistic based on ranks

Wilcoxon signed-ranks test

Alternative to paired t-test, compares 1 group measured twice before to after

Kruskal-Wallis H test

Alternative to anova, compares 3 or more independent groups

Chi-Square test of goodness of fit

Compares observed and expected frequencies

Spearman rho

Alternative to pearson correlation, measures the relationship between 2 ranked variables

Chi-Square test or independence

Determines the association between twocategorical variables

Parametric

Used when data are normally distributed, the sample size is large, data are interval or ratio, you want more powerful results

Non parametric

Used when data are not normally distributed, sample size is small, data are ordinal or nominal, there are outliers or skewed data

Encoding

Determines correct statistical test, prevents wrong conclusions, ensures valid results

Friedman test

Is a non-parametric test used to compare three or more related groups or repeated measurements when data are not normally distributed

Friedman test

It is the non-parametric alternative to repeated measures anova and compares the ranks of scores rather than means

Friedman test

It helps analyze repeated data when parametric assumptions are not met

Repeated measures ANOVA

Is a parametric test used to compare the means of three or more repeated measurements from the same participants

Repeated measures ANOVA

It is used when data are normally distributed, making it suitable for studies with a repeating cycle or repeated observations

Repeated measures ANOVA

It helps determine whether significant changes occur over time within the same group

Parametric tests

These tests assume your data is normally distributed and uses continuous scales, they generally rely on the mean and standard deviation

Non parametric tests

These tests are distribution-free, they don't care about the mean; instead, they usually rank the data from smallest to largest and analyze the positions, the median