2) An Industrial/Organizational Psychologist plans a study on cortisol levels (a measure of stress) in corporate CEOS before versus after a critical meeting to avoid a hostile takeover by a larger company. She measures cortisol levels twice in each of the 24 randomly selected CEOS from Silicon Valley, once before and once after the meeting. She predicts that cortisol levels after the meeting will be different relative to before.

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**Transcript and Explanation:**

**Study on Cortisol Levels in Corporate CEOs**

An Industrial/Organizational Psychologist is planning a study focusing on cortisol levels, a biological measure of stress, in corporate CEOs. The research aims to assess stress levels before versus after a critical meeting. This meeting is vital as it is intended to prevent a hostile takeover by a larger company.

**Study Details:**

- **Sample Group:** The study involves 24 randomly selected CEOs from Silicon Valley.
- **Measurements:** Cortisol levels are measured twice in each CEO. The first measurement takes place before the critical meeting, and the second measurement is conducted afterward.
- **Hypothesis:** The psychologist predicts that the cortisol levels post-meeting will differ from those measured before the meeting.

This study seeks to understand the impact of high-stakes corporate events on the stress levels of top executives.
Transcribed Image Text:**Transcript and Explanation:** **Study on Cortisol Levels in Corporate CEOs** An Industrial/Organizational Psychologist is planning a study focusing on cortisol levels, a biological measure of stress, in corporate CEOs. The research aims to assess stress levels before versus after a critical meeting. This meeting is vital as it is intended to prevent a hostile takeover by a larger company. **Study Details:** - **Sample Group:** The study involves 24 randomly selected CEOs from Silicon Valley. - **Measurements:** Cortisol levels are measured twice in each CEO. The first measurement takes place before the critical meeting, and the second measurement is conducted afterward. - **Hypothesis:** The psychologist predicts that the cortisol levels post-meeting will differ from those measured before the meeting. This study seeks to understand the impact of high-stakes corporate events on the stress levels of top executives.
### Independent Samples t-test

#### Formula:
\[ t = \frac{\sum D}{\sqrt{n(\sum D^2) - (\sum D)^2} \,/\, (n - 1)} \]

- **n** = number of pairs of scores (e.g., if 8 people are measured at time 1 and time 2, df = 8-1 = 7)
- **D** = difference between each pair of scores
- \(\sum D\) = sum of the differences
- \((\sum D)^2\) = square of the sum of differences
- \(\sum (D^2)\) = sum of the differences squared

#### t score:
##### Formula for Independent Samples t-test (degrees of freedom = \((n_1 - 1) + (n_2 - 1)\)):
\[ t = \frac{\bar{X}_1 - \bar{X}_2}{\sqrt{\frac{s_1^2}{n_1 - 1} + \frac{s_2^2}{n_2 - 1}}} \]

- \(\bar{X}_1\) = mean of first group (sample)
- \(\bar{X}_2\) = mean of second group (sample)
- \(s_1^2\) = sample variance of first group
- \(s_2^2\) = sample variance of second group
- \(n_1\) = number of subjects in the first group
- \(n_2\) = number of subjects in the second group

**Note**: Be careful about computing the denominator; pay attention to whether you are working with sample variances or standard deviations to ensure computations are correct.

### One Way ANOVA (see ANOVA table for degrees of freedom)

#### Between Groups Sum of Squares:
Subtract the grand mean from each group mean, square the deviation, multiply by n in each group, and add the values together.
\[ SS_B = \sum n (\bar{X}_A - \bar{X}_G)^2 \]

- **n** = the number of subjects or observations in a group
- \(\bar{X}_A\) = the mean for any group (1 through n) of subjects
- \(\bar{X}_G\) = the overall, or grand, mean for all subjects or observations
Transcribed Image Text:### Independent Samples t-test #### Formula: \[ t = \frac{\sum D}{\sqrt{n(\sum D^2) - (\sum D)^2} \,/\, (n - 1)} \] - **n** = number of pairs of scores (e.g., if 8 people are measured at time 1 and time 2, df = 8-1 = 7) - **D** = difference between each pair of scores - \(\sum D\) = sum of the differences - \((\sum D)^2\) = square of the sum of differences - \(\sum (D^2)\) = sum of the differences squared #### t score: ##### Formula for Independent Samples t-test (degrees of freedom = \((n_1 - 1) + (n_2 - 1)\)): \[ t = \frac{\bar{X}_1 - \bar{X}_2}{\sqrt{\frac{s_1^2}{n_1 - 1} + \frac{s_2^2}{n_2 - 1}}} \] - \(\bar{X}_1\) = mean of first group (sample) - \(\bar{X}_2\) = mean of second group (sample) - \(s_1^2\) = sample variance of first group - \(s_2^2\) = sample variance of second group - \(n_1\) = number of subjects in the first group - \(n_2\) = number of subjects in the second group **Note**: Be careful about computing the denominator; pay attention to whether you are working with sample variances or standard deviations to ensure computations are correct. ### One Way ANOVA (see ANOVA table for degrees of freedom) #### Between Groups Sum of Squares: Subtract the grand mean from each group mean, square the deviation, multiply by n in each group, and add the values together. \[ SS_B = \sum n (\bar{X}_A - \bar{X}_G)^2 \] - **n** = the number of subjects or observations in a group - \(\bar{X}_A\) = the mean for any group (1 through n) of subjects - \(\bar{X}_G\) = the overall, or grand, mean for all subjects or observations
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