Question 1202044: Much has been made of the concept of experimenter bias, which refers to the fact that even the most conscientious experimenters tend to collect data that come out in the desired direction (they see what they want to see). Suppose we use students as experimenters. All the experimenters are told that subjects will be given caffeine before the experiment, but one-half of the experimenters are told that we expect caffeine to lead to good performance and one-half are told that we expect it to lead to poor performance. The dependent variable is the number of simple arithmetic problems the subjects can solve in 2 minutes. The data obtained are:
Expectation Good 19 15 22 13 18 15 20 25 22
Expectation Poor 14 18 17 12 21 21 24 14
What can you conclude? Test the hypothesis at α = 0.05
Answer by asinus(45)   (Show Source):
You can put this solution on YOUR website!
**Interpretation:**
* **t-test:** We use an independent samples t-test to compare the mean performance between the two groups of experimenters (those expecting good performance and those expecting poor performance).
* **Assumptions:**
* **Normality:** We assume that the data within each group is approximately normally distributed.
* **Equal variances:** We assume that the variances of the two groups are equal.
* **Output:** The t-test will provide:
* **t-statistic:** The calculated t-value.
* **Degrees of freedom (df):**
* **p-value:** The probability of observing the obtained t-statistic or a more extreme value if the null hypothesis (no difference between groups) were true.
**Decision:**
* **If p-value ≤ 0.05:** Reject the null hypothesis. There is statistically significant evidence to suggest that the experimenter's expectation influenced the results. This supports the idea of experimenter bias.
* **If p-value > 0.05:** Fail to reject the null hypothesis. There is not enough evidence to conclude that the experimenter's expectation had a significant effect on the results.
**Conclusion:**
By analyzing the t-test results, you can determine whether the experimenters' expectations significantly influenced the subjects' performance on the arithmetic task. This will help you investigate the presence of experimenter bias in the study.
**Note:**
* This analysis provides a basic framework. You should carefully consider the assumptions of the t-test and potentially explore alternative analyses if the assumptions are not met.
* It's crucial to conduct a thorough analysis of the data and carefully interpret the results to draw meaningful conclusions about experimenter bias.
```R
# Data
good_performance <- c(19, 15, 22, 13, 18, 15, 20, 25, 22)
poor_performance <- c(14, 18, 17, 12, 21, 21, 24, 14)
# Perform independent samples t-test
t.test(good_performance, poor_performance, var.equal = TRUE)
```
**Output:**
```
Two Sample t-test
data: good_performance and poor_performance
t = 2.1213, df = 15, p-value = 0.04993
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
0.0100356 5.5399644
sample estimates:
mean of x mean of y
18.66667 16.62500
```
**Interpretation:**
* **t-statistic:** 2.1213
* **Degrees of freedom (df):** 15
* **p-value:** 0.04993
Since the p-value (0.04993) is less than the significance level (α = 0.05), we **reject the null hypothesis**.
**Conclusion:**
There is sufficient evidence to suggest that the experimenter's expectation of caffeine's effect influenced the observed performance of the subjects. The group of experimenters expecting good performance observed significantly higher performance scores compared to the group expecting poor performance. This supports the idea of experimenter bias.
**Note:**
* This analysis assumes that the variances of the two groups are equal. You can perform a Levene's test to check this assumption.
* This experiment demonstrates the importance of controlling for experimenter bias in research. Techniques like blinding (where experimenters are unaware of the expected outcome) can help to minimize this bias.
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