8. One of the most common tools of the cognitive psychologist is the lexical dec

Question

8. One of the most common tools of the cognitive psychologist is the lexical decision task, in which a string of letters is flashed on a screen and an experimental participants must decide as quickly as possible whether those letters form a word. This task is often used as part of a more complex experiment, but this exercise considers reaction time as a function of the number of letters in a string for a single participant. The following data represent the participant's reaction times in response to three strings of each of four lengths: 3, 4, 5, or 6 letters. Calculate Pearson's correlation coefficient for the data and test for statistical significance.

               Number of Letters           Reaction Time in

     Trial No.        in String                 Milliseconds

            1                      6                                  930

            2                      5                                  900

            3                      3                                  740

            4                      5                                  820

            5                      4                                  850

            6                      4                                  720

            7                      3                                  690

            8                      6                                  990

            9                      4                                  810

            10                     3                                  830

            11                     6                                  880

            12                     5                                  950

  8a. Use the correlation coefficient calculated in the above exercise to find the regression equation for predicting reaction time from the number of letters in the string.

8b. How many milliseconds are added to the reaction time for each letter added to the string?

Explanation / Answer

Pearson correlation of no of letters in string and reaction time = 0.795(By using minitab software)

Testing the significance of pearson's correlation coefficient:

H0: corr. coef (P)=0 Vs H1: P not equal to 0.

test statistic t= (r* sqrt(n-2))/sqrt(1-r^2)

where r:sample correlation coefficient

        n:sample size

By Minitab p-value comes out to be 0.002,which means if we take alpha=0.05,then with 95% confidence we can say that we reject H0 and conclude that correlation coefficient is not equal to 0.

8.a)

The regression equation is:
Reaction time = 556 + 63.7*no of letters in string

Predictor                  Coef      SE Coef     T      P
Constant                  556.00    71.26      7.80 0.000
no of letters in string   63.67    15.37     4.14 0.002

S = 59.5175   R-Sq = 63.2%   R-Sq(adj) = 59.5%

Since the correlation coefficient was close towards 1,hence it can be seen that there is a highly/strong positive relation between the concerned two variables. Hence with increase in No of strings, reaction time is bound to increase which is shown in the regression equation.

8.b) For adding each letter to the string,63.7 milliseconds is added to the reaction time,since the slope denotes that.

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