Question

Rewards and creativity Do external rewards—things like money, praise, fame, and grades—promote creativity? Researcher Teresa Amabile suspected that the answer is no, and that internal motivation enhances creativity. To find out, she recruited 47 experienced creative writers who were college students and divided them at random into two groups. The students in one group were given a list of statements about extrinsic reasons (E) for writing, such as public recognition, making money, or pleasing their parents. Students in the other group were given a list of statements about intrinsic reasons (I) for writing, such as expressing yourself and enjoying playing with words. Both groups were then instructed to write a poem about laughter. Each student’s poem was rated separately by 12 different poets using a creativity scale.30 These ratings were averaged to obtain an overall creativity score for each poem. The table shows summary statistics for the two groups.

We used software to randomly reassign the 47 subjects to the two groups 100 times, assuming the treatment received doesn’t affect each individual’s creativity rating. A dot plot of the simulated difference (Intrinsic−Extrinsic)$\frac{305}{1526}=0.200=20.0\%(\mathit{I}\mathit{n}\mathit{t}\mathit{r}\mathit{i}\mathit{n}\mathit{s}\mathit{i}\mathit{c}\mathbf{-}\mathit{E}\mathit{x}\mathit{t}\mathit{r}\mathit{i}\mathit{n}\mathit{s}\mathit{i}\mathit{c}\mathbf{)}$

in mean creativity, rating is shown.

a. Why did researchers randomly assign the subjects to the two treatment groups?

b. Estimate and interpret the P-value.

c. What conclusion would you make?

d. Based on your conclusion in part (c), could you have made a Type I error or a Type II error? Justify your answer.

Short answer

Part a) This is necessary because otherwise, we would not be able to tell whether the differences observed after the treatments are due to the treatments themselves or to differences between the groups that existed prior to the treatments.

Part b) There is $1\%$the probability of getting similar sample results or more extreme results when there is no difference in the mean creativity rating of the intrinsic rewards and the mean creativity rating of the extrinsic rewards.

Part c) The claim that intrinsic rewards promote creativity more than extrinsic rewards is backed up by compelling evidence.

Part d) Type I error

Step-by-step solution

Part a) Step 1: Explanation

The subjects were assigned to the two treatment groups at random so that the groups were as similar as possible before the treatments.

This is necessary because otherwise, we would not be able to tell whether the differences observed after the treatments are due to the treatments themselves or to differences between the groups that existed prior to the treatments.

Part b) Step 1: Given information

$$\begin{gathered} {\overline{x}}_1=19.883 \\ {\overline{x}}_2=15.739 \end{gathered}$$

The claim is that the intrinsic group has a higher mean creativity rating.

Part b) Step 2: Explanation

Either a null hypothesis or an alternative hypothesis is asserted.

$$\begin{gathered} H_0:{\mu }_1={\mu }_2 \\ {H}_0:{\mu }_1>{\mu }_2 \end{gathered}$$

Where,

${\mu }_1=$true mean creativity rating for the Intrinsic group.

${\mu }_2=$true mean creativity rating for the Extrinsic group.

As a result, the difference in sample means is,

$$\begin{gathered} {\overline{x}}_1-{\overline{x}}_2=19.883-15.739 \\ =4.144 \end{gathered}$$

When the null hypothesis is true, the $P$-value is the probability of getting the sample results or more extreme results.

Therefore, we note that $1$of the $100$dots lies to the right of $4.144$then, we have,

$$\begin{gathered} P-value=\frac{1}{100} \\ =0.01 \\ =1\% \end{gathered}$$

Therefore, when there is no difference in the mean creativity rating of intrinsic rewards and the mean creativity rating of extrinsic rewards, we conclude that there is a $1\%$ chance of getting similar sample results or more extreme results.

Part c) Step 1: Explanation

From part (b) we have,

we note that 1 of the 100 dots lies to the right of $4.144$then, we have,

$P-value=1\%$

And we know that the null hypothesis is rejected if the P-value is less than or equal to the significance level.

$P<0.05\Rightarrow \text{Reject}{H}_0$

Therefore, we conclude that the claim that intrinsic rewards promote creativity more than extrinsic rewards is supported by compelling evidence.

Part d) Step 1: Explanation

Part (c) of our conclusion states, "There is compelling evidence to support the claim that intrinsic rewards promote creativity more than extrinsic rewards."

When we reject a null hypothesis when the null hypothesis is true, we make a type I error. When we fail to reject the null hypothesis when the null hypothesis is false, we make a Type II error.

As a result, if we reject the null hypothesis, we have made a Type I error.