The summary table for the model is as follows:

Summary table of the model predicting the number of zombies incapacitated from the weapon used

Let's see how we calculate these values.

Calculate the sum of squared errors

First, we compute the total sum of squares:

We arrive at this value by subtracting the grand mean from each score, squaring these differences and adding them up, as shown in the following tables:

Next, we calculate the model sum of squares:

Next, we calculate the residual sum of squares:

For each score we compute the difference between the score and the group mean, then square these differences and sum them, as shown in the following table:

Residual sum of squares for the Taser group

Residual sum of squares for the rTMS group

Residual sum of squares for the garlic group

Calculate the mean squared errors

We convert the sums of squares to mean squares by dividing by the degrees of freedom for each:

Calculate F

We calculate F as follows:

Conclusion

There was a significant difference in the mean number of zombies incapacitated by different weapons, F(2, 12) = 14.70, p < 0.001.

The contrasts and weights reflecting Zach's predictions are in the following table:

Contrasts and weights for Zach's two hypotheses

 

Omega-squared

Cohen's d

Cohen’s d is defined as:

The pooled estimate of the standard deviation is:

The values and resulting calculations are tabulated below:

Cohen's d for pairwise comparisons of group means

The summary table for the model is as follows:

Summary table of the model predicting the belief in the product from the dose of oxytocin administered before the speech

Let's see how we calculate these values.

Calculate the sum of squared errors

First, we compute the total sum of squares:

We arrive at this value by subtracting the grand mean from each score, squaring these differences and adding them up, as shown in the following tables:

Next, we calculate the model sum of squares:

Next, we calculate the within-participant sum of squares by calculating the sum of squared error within each participant and adding them up:

The sum of squared error for each participant is shown in the following table:

Table showing the sum of squared errors within each participant

Next, we calculate the residual sum of squares:

Calculate the mean squared errors

We convert the sums of squares to mean squares by dividing by the degrees of freedom for each:

Calculate F

We calculate F as follows:

Conclusion

There was a significant difference in the belief scores after different doses of oxytocin, F(2, 12) = 8.54, p = 0.005.

• There were five groups being compared (code 1318, scientists, security, professional services and technicians), so the degrees of freedom for the model will be 4 ()
• The total degrees of freedom will be: 
• The residual degrees of freedom will be: 
• We can work out the mean squared error for the model by dividing the sum of squares by the degrees of freedom: 
• We can work out the residual sum of squared errors by multiplying the mean squared error by the degrees of freedom: 
• We can work out the total sum of squares by adding the model and residual sum of squares: 
• The F statistic is the mean squared error for the model divided by that for the residual: 

• There were five groups being compared (code 1318, scientists, security, professional services and technicians), so the degrees of freedom for the model will be 4 ()
• The total degrees of freedom will be: 
• The residual degrees of freedom will be: 
• We can work out the model sum of squares by subtracting the residual sum of squares from the total sum of squares: 
• We can work out the mean squared error for the model by dividing the sum of squares by the degrees of freedom: 
• We can work out the mean squared error for the residual by dividing the sum of squares by the degrees of freedom: 
• The F statistic is the mean squared error for the model divided by that for the residual: 

The summary table for the model is as follows:

Summary table of the model predicting openness to a new relationship after studying different prompt lists

 

Let's see how we calculate these values.

Calculate the sum of squared errors

First, we compute the total sum of squares:

We arrive at this value by subtracting the grand mean from each score, squaring these differences and adding them up, as shown in the following tables:

Next, we calculate the model sum of squares:

Next, we calculate the within-participant sum of squares by calculating the sum of squared error within each participant and adding them up:

The sum of squared error for each participant is shown in the following table:

Table showing the sum of squared errors within each participant

Next, we calculate the residual sum of squares:

Calculate the mean squared errors

We convert the sums of squares to mean squares by dividing by the degrees of freedom for each:

Calculate F

We calculate F as follows:

Conclusion

There was a significant difference in the openness to a new relationship after different prompts to thing about pros and cons of relationships, F(2, 8) = 6.00, p = 0.026.

The Bayes factor is 5.08, which means that the data are 5.08 times more likely given the alternative hypothesis compared to the null hypothesis. In other words, we should shift our belief in the alternative hypothesis (that these prompts change openness to new relationships) relative to the null by a factor of 5.08. This value 'has substance' but is not at all strong evidence for the alternative hypothesis (relative to the null). In other words we should shift our belief that these prompts change openness to new relationships a little, but not very much.

The second experiment in Alice’s report (Alice's Lab Notes 16.1), when Zach reanalysed it, seemed to suggest that sending visual images to someone’s ID chip while they recalled a memory would interfere with it (i.e., result in lower recall of the event). Roediger decided to do a follow-up study. He took 18 participants: 6 of them received no memory interference while they recalled an event, 6 received visual interference unrelated to the event they were recalling, and 6 received visual interference related to the event they were recalling. The data are in Table 16.15. Compute the F-ratio. Were there significant differences in recall between the three groups?

summary table for the model is as follows:

Summary table of the model predicting memory recall from the type of interference

Let's see how we calculate these values.

Calculate the sum of squared errors

First, we compute the total sum of squares:

We arrive at this value by subtracting the grand mean from each score, squaring these differences and adding them up, as shown in the following tables:

Table continues below

Next, we calculate the model sum of squares:

Next, we calculate the residual sum of squares:

For each score we compute the difference between the score and the group mean, then square these differences and sum them, as shown in the following table:

Residual sum of squares for the no interference group

Residual sum of squares for the unrelated interference group (continued below)

Residual sum of squares for the related interference group

Calculate the mean squared errors

We convert the sums of squares to mean squares by dividing by the degrees of freedom for each:

Calculate F

We calculate F as follows:

Conclusion

There was a significant difference in the mean recall after different types of interference, F(2, 15) = 12.80, p < 0.001.

The Bayes factor is 51.57, which means that the data are 51.57 times more likely given the alternative hypothesis compared to the null hypothesis. In other words, we should shift our belief in the alternative hypothesis (that the type of interference affects memory) relative to the null by a factor of 51.57 This value is strong evidence for the alternative hypothesis (relative to the null). In other words we should shift our belief that the type of interference affects memory a fair amount.