Correlation and Regression Stats

T-Test Recap T Test is used to compare two categories of data – Ex. Size of finch beaks on Baltra island vs. Isabela island – Ex. Heights of boys vs. girls – Ex. (add your own)

Regression Stats A regression is used to test for a correlation in data – Ex: Are higher math MAPS scores related to a higher grade in algebra class? – Ex: Are the lengths of women’s boots related to the temperature outside? – Ex: Add your own

*correlation means that there is a relationship between the two sets of data, it DOES NOT necessarily mean that one causes the other. – MAP scores don’t cause a higher grade in algebra, and women’s boot lengths don’t control the weather

Question: As you go further up in the atmosphere do temperatures become colder? Independent variable: Dependent variable: *In order to test for a correlation there has to be at least 5 different values for the independent variable

The best way to visualize a relationship between two sets of data is with a scatter plot and a line of best fit Altitude (km)Temp (°C) *Add a line of best fit to the chart Is this a linear relationship (correlation)? Is is a positive or negative relationship (correlation)?

Create a scatter graph for the data: Open up an Excel spreadsheet Copy and paste the table data into the workbook Highlight the numbers and insert a marked scatter graph Back click on one of the data points to add a trendline click the option tab and add the equation of the line Copy and paste your graph into the next slide

How close was your line of best fit compared to Excel’s? Looking at the equation of the line, can you tell me on average how temperature changed for every km rise in in altitude?

*Our altitude data seemed to have a negative linear correlation: as altitudes got higher, temperatures dropped. But…. 1.Is there really a significant correlation? 2.If there is a correlation how strong or weak is it?

1. Is there a significant correlation? If the p-value is below 0.05 there is a significant correlation between the two data sets. *It means that we have 95% certainty that there is a relationship between the two variables

2. How strong is the correlation? The strength of the correlation can be measured as a value between 1 and -1 (called an R – value) 1 is a 100% (very strong) positive correlation -1 is a 100% (very strong) negative correlation 0 is a 0% correlation (no correlation or no relationship between your variables)

Look back at your altitude/temperature graph… with your partner estimate a correlation strength and write it here: R value = *Was it positive or negative? Why? *Was it close to zero or close to 1 (or -1)? Why?

Time to test! Download the excel sheet called ‘Regression Test’ Open the workbook and select the tab called “input” Input in your values from the boot/temp table Click the tab that says “output” Although these tables have a lot of information in them, we will only be looking at several numbers from the first two tables…. NOTE: pay attention to how excel is displaying decimals (period or comma) and ensure you keep the same format when entering in data

Standard deviation of the average – how much the data points vary from the average P-value: the probability of no correlation again this needs to be below 0.05 to indicate a significant correlation Average change in Y value for every unit of the X value (is the same number as the slope in the equation of the line) … For our example, how much the temperature changes as altitude increase by 1 km. R - The correlation strength: the “puffiness” of the scatterplot. A strong correlation has a value close to 1 or -1. A weak correlation has a value close to 0 R 2 Value: What you report in your formal conclusion. (Literally the R value squared, to get rid of the negative for clarity).

Write the p-value here: Is there a significant correlation between altitude and temperature? How do you know? Write the r-value here: Is there a strong correlation between altitude and temperature? How do you know?

Time to Conclude! Formal results makes a clear and direct statement about the outcome your statistical test while reporting key statistics: “The temperature changed an average of -0.3±0.04 °c per kilometer rise in altitude. This marks a significant temperature decrease as altitude increases in this study (p=0.0052, n=5) There is a strong, negative correlation between altitude and temperature (r 2 = )

Note: Multiple Trials AltitudeTemp When you have multiple trials, your data table should still be in two columns for excel to present and process the data correctly.