Psychology Textbook Unit 8 Scatterplots and Correlational Analysis in R

Unit . and Correlational Analysis CASTRO Summary . In this unit you will learn how to create and how to calculate Pearson correlation coefficient with You will learn how to enter the code and how to interpret the output that provides . Prerequisite Units Unit . Statistics with Introduction and Descriptive Statistics Unit . to Statistical Significance Unit . Measures Reading Data and Creating a We have the of 50 participants with different amount of experience ( from to 16 weeks ) in performing a computer task , and their accuracy ( from to 100 correct ) in this task . Thus , Experience is the predictor variable , and Accuracy is the outcome variable . The code line below imports our by using the 91

function , and assigns the data file to the object read data file ( header TRUE , sep , Once has access to your data file , you can create a . There are multiple ways a in ( links are included below ) Some ways are quick and simple , so you can easily see the graphical representation of how your variables of interest are related other ways require some additional packages Let see here two frequently used options . Using plot function For the simplest , you just need to specify the two variables that you want to plot . The first one will be on the and the second one on the . Remember that you need to specify , with the sign , that your variables , Experience and Accuracy , are within the object . basic plot ( Experience , Accuracy ) 92

This is the that you will obtain oo . I 10 15 The plot function has a number of possibilities to modify and improve the basic . For example basic plot ( Experience , Accuracy , main Relationship between Experience and Accuracy , 21 , blue , Experience , Accuracy ) The main argument allows you to include a title to the . You can also choose the shape ofthe points , with Correlations in 93

( you can find the assignment of shapes to numbers in the links included below ) and the color , with . In addition , you can change the labels to the axis , with and . Ifyou run the script above , you will obtain Relationship between Experience and Accuracy oE . as go . 00 I 10 15 Experience Find more options and information here . Using the package First of all , you will need to install the package for . And , as indicated in the first line of code below , you will to load it when you want to use it , using the library function . 94

load the package library ( basic ( aes ( Experience , Accuracy ) print ( In this script , you are just indicating the variables in the and , and that the data are represented by points . To visualize the , you have to use print . If you run the script above , you will obtain a a . a '

You can elaborate on this , and improve as much as you want . The script below shows you some options to modify the data points ( with ) titles ( and ) changes to the scales of the axis ( and ) including the regression line ( and modifying the text elements with theme load the package library ( more elaborated ( aes ( Experience , Accuracy ) size , dark grey , shape 21 ) Relationship between Experience and Accuracy ) Experience ) Accuracy ) 18 ) se FALSE , color red , weight ) theme ( black , lain ) black , lain )

( black , old ) black , old ) black , old ) fill ) black , size ) print ( Running this script , you will obtain Accuracy Relationship between Experience and Accuracy 100 90 80 70 60 50 10 15 97 You have plenty of options to improve the visual aspects ofyour . Find more in the following websites How to make a with wil i visualization 2020 lot How to make any plot using Correlational Analysis Once you have a visual representation of how your variables are related , it is time to conduct the correlational analysis that will allow you to obtain Pearson correlation coefficient between your variables of interest . In , you can use the cor function , as you can see in this code line how to obtain Pearson cor ( Experience , The output will give you Pearson Simply 98 Correlations in

To obtain the result of the statistical significance test and the confidence intervals for the correlation coefficient , you can use contest how to obtain Pearson with significance test and confidence intervals ( Experience , Accuracy ) You will obtain the following output Pearson correlation data Experience and Accuracy , 48 , alternative hypothesis true correlation is not equal to 95 percent confidence interval sample estimates

The null hypothesis in a correlation test is a correlation of , that is , that there is no relationship between the variables of interest . As indicated in the output above , the alternative hypothesis is that that the correlation coefficient is different from zero . The statistic tests whether the correlation is different from zero . We have not seen the statistic yet , so you only need to pay attention to the value . As we explained here , the value for a hypothesis test to be statistically significant is 005 , so that if the is less than , then the result is statistically significant . Here , the is very small uses the scientific notation for very small quantities , and that why you see the in the number For values larger than , will give you the exact value . You just need to know that this number , represents a very small value , much smaller than 005 so , we can conclude that the correlation between Experience and Accuracy is statistically significant . In the last line you can see Pearson correlational coefficient , indicating a very strong correlation . And , above , the 95 confidence interval for the correlation coefficient . Following APA style , we typically report the confidence interval this way 95 CI , So , we obtained an of in our sample , with a 95 CI between and . That is , you can be 95 confident that the true in the population is between the values of and . This interval is relatively narrow , and any value within the interval would indicate a very strong correlation , so we have a very accurate estimation ofthe correlation in the population . 100

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