Introduction:This learning lab is very similar to last week's learning lab. We will look at the same data but now analyze them as if they came from a study in which each individual completed every condition. After performing the analyses, you will compare the results to the results we obtained in the previous learning lab. The goal of this exercise is to give you a sense of the differences between independent sample and related sample designs.

The data in Excel:Open the file 'PSYCH200_Lesson_10_Learning_Lab.xlswith Excel.

You should see two datasets, which were obtained from the same set of individuals. Let's again imagine that these data come from an experiment in which a researcher aimed to determine whether reading a chapter first and then going to a lecture is a better learning method than going to a lecture first and then reading the chapter.

To address this question, the researcher recruited 25 people, and subjected each individual to the reading then lecture condition (condition 1) and to the lecture then reading condition (condition 2).

The order of these conditions was randomized to make sure that any differences that could be found between these methods is not due to the fact that people had more practice for the second condition they performed. Again, the researcher assessed learning by having each participant complete a test on the material afterwards. In this case, two different sets of materials were used to avoid that people were tested on the same material twice. Column A of the Excel sheet displays the scores for condition 1, and column B displays the scores for condition 2.

Step 1: Calculate the t-value for the data set

Based on the two datasets, we will calculate the t-value in cell G13. For this, we use the paired sample t-test procedure. Here is the formula:

t=M

D

D

s

MD

t=MDDsMD

Let's break this down into smaller steps:

Step 1a:MDand D

First, calculate the difference score for each individual by subtracting the score in condition 1 from the score in condition 2. Put the difference scores in cells C2 to C26. Calculate the mean difference score and put the result in cell H2.

Usually, no difference is predicted between two conditions based on the null hypothesis H0. Thus, D= 0. This is displayed in cell G4.

Step 1b: sMD

In the next step, we need to calculate the standard error of the mean. For this, we use the following formula:

s

MD

=s

n

sMD=sn

Let's break this down into its components. First, we need to calculate the variance s2so we can calculate the standard deviation s. Here is the formula for calculating the variance s2:

s

2

=SS

n1

=SS

df

s2=SSn1=SSdf

Calculate the sum of squares. You will do this the same way you calculated SS for t-scores (i.e., LL8 and LL9). First, subtract each difference scores from the mean difference score in column D. Then, square these values to get the squared deviations from the mean difference in column E. Sum these values and put the answer in cell H5.

Put the degrees of freedomdfin cell H6.

Now we can calculate the variance. Do so in cell H7.

Next, take the square root of the variance s2to get the standard deviation s. Put the result in cell H8.

s=s

2

s=s2

Finally, to get sMD, take the standard deviation s, and divide it by the square root of the number of difference scores n. Put the result in cell H9.

s

MD

=s

n

sMD=sn

Step 1c: T-value

Calculate the value for t based on the quantities you calculated in the previous steps. Again, use the following formula for t:

t=M

D

D

s

MD

t=MDDsMD

Save your work

Step 2: Determine the one-tailed and two-tailed probabilities

As we saw in the previous lesson, Excel has a build-in function to calculate probabilities with a t-test. This function is called =TTEST(). This function takes four input arguments; the data for the first condition (array 1), the data for the second condition (array 2), whether the test is one-tailed or two-tailed (nondirectional), and the type of test.

One-tailed probability test

We will calculate the one-tailed probability for the paired sample t-test in cell H16.

For array 1, you want to select the data for condition 1 (cells A2:A26. For array 2, you want to select the data for condition 2 (cells B2:B26).

First, we will do a one-tailed (directional) test of the null hypothesis H0. To do so, put in the value 1 for Tails. For Type, put in the value 1. This corresponds to a paired sample t-test.

Thus, the formula in cell H16 should say= TTEST(A2:A26,B2:B26,1,1). A probability should appear in cell H16 after you hit Enter.

Two-tailed probability test

Now, perform a two-tailed probability test on the data by adjusting the formula for the t-test and putting the answer in cell H17.

Save your work

Step 3: Making inferences

Based on the probabilities you found for the one-tailed and two-tailed t-test, answer questions Q1 and Q2 in cells I16 and I17. Put your Yes/No answer in cells J16 and J17.

Save your work

Step 4: Comparing the independent sample and paired sample t-test

Finally, go back to the previous learning lab and review the results. Compare them to the results you got in this learning lab. You should find that even though the data were the same in the two cases, the result of the t-test is different.

Answer question Q3 displayed in cells I19 and I20 by putting your Yes/No answer in cell J20

AutoSave . Off) PSYCH200_LL10_WILLIAMS - Compatibility Mode - Saved Tasha-Gaye Tracey X File Home Insert Page Layout Formulas Data Review View Help Search Share Comments AutoSum LO Calibri - 11 AA = ab Wrap Text General Fill AY O Paste BIU - a . A . Merge & Center . $ -% " Conditional Format as Cell Insert Delete Format Ideas Formatting Table Styles Clear Sort & Find & Filter * Select Ideas Clipboard G Font Alignment Number G Styles Cells Editing BH X V A B C D E F G H J K L M N 0 P Q Condition 1 Condition 2 X2 - X1 (D) MD - D (MD - D) 90 35 -5 1.52 2.3104 Mean X2-X1 (MI -6.52 70 65 -10 3.48 12.1104 63 53 -10 3.48 12.1104 Ho difference 0 85 64 -21 14.48 209.6704 SS 4488 77 65 -12 5.48 30.0304 24 19 -25.52 651.2704 00 45 64 75 59 -16 9.48 89.8704 73 63 -10 3.48 12.1104 SMO 10 75 -10 3.48 12.1104 62 - 2 4.52 20.4304 68 17 -23.52 553.1904 35 -30 23.48 551.3104 T value -11.52 132.7104 -14.52 210.8304 T-test probability -16.52 272.9104 One-tailed: Q1: Based on a one-tailed test with a = .05, the researcher would reject Ho Y/N -18.52 342.9904 Two-tailed: Q2: Based on a two-tailed test with a = .05, the researcher would reject Ho Y/N -33 26.48 701.1904 - 5 1.52 2.3104 Q3: From comparing the results from this week to last week, -13 6.48 41.9904 a paired sample t-test has more power than an independent sample t-test Y/N 70 - 6 -0.52 0.2704 57 -18 11.48 131.7904 60 - 5 -1.52 2.3104 76 -14.52 210.8304 65 -15 8.48 71.9104 53 21 14.48 209.6704 Sheet1 Sheet2 Sheet3 + Mail " -- + 80% 8:45 PM O Type here to search N 99 X 7/7/2019