PSY 321:  Cognitive Processes
Mental Rotation

1. Copy the above table (drag the mouse downward, starting just to the right of the colon after Raw Data Set to the beginning of the decorative divider, and then use the copy command) and paste it into Excel.
2. Identify the column that contains the angle of rotation information (usually column C).
3. Identify the column that contains the mirror image reaction time (usually column E).
4. Identify the first row that contains data (usually row 6).
5. Identify the last row that contains data.
6. In any empty cell, enter the following formula:
   
   =CORREL($C$6:$C$21, E6:E21)
   
   Replace both letters C with the column you identified in step 2, both letters E with the column you identified in step 3, both numbers 6 with the row you identified in step 4, and both numbers 21 with the row that you identified in step 5.
   The value in this cell is the correlation coefficient between the angle of rotation and the mean reaction time for the mirror image pairs.
7. In the cell below the cell you used in step 6, enter the following formula:
   
   =COUNT(E6:E21)-2
   
   Replace both letters E with the column you identified in step 3, 6 with the row you identified in step 4, and 21 with the row that you identified in step 5.  This cell gives the degrees of freedom, which are needed for the following steps.
8. In the cell below the cell you used in step 7, enter the following formula:
   
   =E24*SQRT(E25)/SQRT(1-E24^2)
   
   Replace both occurrences of E24 with the column and row of the cell that you used in step 6 (the correlation coefficient).  Replace E25 with the column and row of the cell that you used in step 7 (the degrees of freedom).  This cell gives the value of the t-test that test the null hypothesis H₀: ρ = 0
9. In the cell below the cell you used in step 8, enter the following formula:
   
   =TDIST(ABS(E26),E25,2)
   
   Replace E26 with the column and row of the cell that you used in step 8 (the t value).  Replace E25 with the column and row of the cell that you used in step 7 (the degrees of freedom.)  This cell gives you the probability that you would expect to see a correlation coefficient this large in the sample when in fact no such correlation exists in the population.  If this value is less than .05, psychologists would typically reject the null hypothesis and conclude that the relationship probably exists in the population.
10. Select the four cells that contain the formulae you just entered in steps 6 through 9.  Copy the cells and paste them into cells two cells to the right (there should be one blank column between the two sets of formulae.)  Be sure to paste the formulae in the same rows as the original.  The values in these cells are the same as the above, except that they are for the identical pairs.
11. When presenting the results one would write:  Pearson's product moment correlation coefficient was calculated for the angle of rotation and reaction time for the mirror image pairs, r = give the value of the correlation coefficient from step 6, t(give the degrees of freedom from step 7) = give the t value from step 8, p = give the probability from step 9, α = .05.
     

1. Copy the above table (drag the mouse downward, starting just to the right of the colon after Raw Data Set by Participant to the beginning of the decorative divider, and then use the copy command) and paste it into Excel.
2. Identify the column that contains the reaction time (RT) for pairs of objects that are mirror images with 0° angle of rotation (usually column D).
3. Identify the first row that contains data.  This is the row immediately below the row that contains "ID  Sex  Age 0  22.5 ...". 
4. Identify the last row that contains data.
5. In an empty cell a couple of rows below the last row that contains data in the column that you identified in step 2, enter the following formula:
   
   =AVERAGE(D7:D11)
   
   Replace both letters D with the column you identified in step 2, 7 with the row you identified in step 3, and 11 with the row you identified in step 4.
   The value in this cell is the mean reaction time for pairs of objects that are mirror images of each other with 0° of rotation.
6. Select the cell that contains the formula you just entered. Copy the cell and paste it into the next seven cells to the right in the same row.  This will create the mean reaction time for mirror image objects for each of the angles of rotation.
7. Skip one column (the blank column between the mirror image and identical RTs) and paste the cell into the next eight cells in the same row.  This will create the mean reaction time for identical objects for each of the angles of rotation.
    
8. Select the cells that have the angles of rotation in them (0, 22.5, 45, ...).
9. While holding down the Contrl key, drag across the average RTs for the eight angles of rotation for the mirror image data.
10. Click on Insert | Scatter | Scatter with Straight Lines and Markers
11. On the Chart Tools | Design ribbon, click Select Data.
12. Click the Add button.
13. In the Series name: text box, type Identical.
14. Click the data select button () to the right of the Series X values: text box.
15. Drag across the eight cells that contain the eight angles of rotation (0, 22.5, 45, etc.) and press Enter.
16. Click the data select button to the right of the Series Y values: text box.
17. Drag across the eight cells that contain the eight mean RTs for the identical data (the means that you created in steps 5 and 6 above) and press Enter.
18. Click OK
19. Click the first Series (Series 1)
20. Click the Edit button.
21. Enter Mirror Image in the Series names box.
22. Click OK
23. Click OK
     
24. On the Chart Tools | Layout ribbon, click on Axis Titles | Primary Horizontal Axis Title | Title Below Axis.
25. Type Angle of Rotation (degrees) and press Enter
26. On the Chart Tools | Layout ribbon, click on Axis Titles | Primary Vertical Axis Title | Rotated Title
27. Type RT (ms) and Press Enter
     
28. On the Chart Tools | Layout ribbon, click on Trendline | Linear Trendline
29. In the Add Trendline dialog box, select Mirror Image and click OK
30. Right click on the trend line that was just added, and select Format Trendline
31. In the Trendline Options, select Custom in the Trendline Name area and enter Mirror Image Regression Line in the box.
32. In the Trendline Options, select Display R-squared value on chart.
33. Click Close
34. Repeat the previous steps (28 through 33) for the Identical series.
     
35. In an empty cell enter a formula similar to:
    
    =COUNTIF(B7:B11,"F")
    
    The "B" represents the column that has the sex data.  The 7 indicates the first row that has data. The 11 indicates the last row that has data. That is, we are asking for the number of the scores in cells B7 through B11 which have the value "F" (e.g. the number of females who participated.)
36. In an empty cell enter a formula similar to:
    
    =COUNTIF(B7:B11,"M")
    
    The "B" represents the column that has the sex data.  The 7 indicates the first row that has data. The 11 indicates the last row that has data. That is, we are asking for the number of the scores in cells B7 through B11 which have the value "M" (e.g. the number of males who participated.)
37. In an empty cell enter a formula similar to:
    
    =AVERAGE(C7:C11)
    
    The "C" represents the column that has the age data.  The 7 indicates the first row that has data. The 11 indicates the last row that has data. That is, we are asking for the mean age in cells C7 through C11 (e.g. the mean age of the participants.)
     
38. Optional: Format the graph into appropriate APA style.  For example:
    1. Remove the border from the graph and chart area
    2. Remove the gridlines from the graph
    3. Make the lines and markers black for both data series
    4. Make the regression/trend lines distinguishable from each other (e.g. make one a dashed line and the other a dot-dash line)
    5. Increase all font sizes to 12 points and remove the bold
    6. Make the graph sufficiently large
    7. Move the R² values to the side, near their respective regression / trend lines

Reload the raw data set

Glossary

Correlation coefficient -- a statistic that tells how strongly two variables are related to each other.  The correlation coefficient that is given by Excel's CORREL function can be interpreted by looking at how close its absolute value, or magnitude, is to +1.  The closer its magnitude is to one, the more strongly the two variables are related to each other.  This means that you can predict the value of one of the variables fairly accurately give the value of the other variable.  If the magnitude is +1, then the prediction will be perfect.  The closer its magnitude is to zero, the less strongly the two variables are related to each other and the less accurate the prediction will be (or one of the assumptions of the correlation has been violated.)  The sign of the correlation coefficient tells you the direction of the relationship.  If the sign is positive, then as the value of one variable increases, the value of the other variable will tend to increase as well.  If the sign is negative, then as the value of one variable increases, the value of the other variable will tend to decrease.

Degrees of freedom -- the number of scores that are free to take on any value after certain constraints (such as the mean of the data set) have been made.

Null hypothesis -- In inferential statistics, the null hypothesis is typically the hypothesis that one wants to reject.  It is the hypothesis that there is no relation between two variables, or that no difference exists between the two variables.  In this experiment, the null hypothesis is H₀: ρ = 0.  The Greek letter ρ is the correlation coefficient in the population.  The null hypothesis says that if we tested everyone, we would find no relation between the two variables that are being correlated.

R²  (R squared) -- the coefficient of determination.  R² tells you the proportion of variability in one variable that is explainable by variation in the other variable.  For this study, how much of the differences in reaction times that we see can be explained by differences in the angle of rotation?  The closer R² is to 1.00, the better we are able to predict the value of one variable given the value of the other variable.

t-test -- an inferential statistic that can be used to determine if a correlation coefficient is likely to be different from 0 (which indicate no relation between the data.)