Provide the effect size and explain the size of the effect S1=8.64S2=5.01 A psychologist aims to determine the effect of instructions on the time required to solve a mechanical puzzle. Twenty volunteers are tasked with solving the same puzzle as quickly as possible. Prior to starting, the subjects are randomly divided into two equal groups, each receiving different sets of instructions. One group is informed that the task is difficult, while the other is told it is easy. The time taken by each subject to solve the puzzle is recorded. The study employs a two-tailed test with a significance level of α = 0.05.**Data**:- **Difficult instruction** group times (in minutes): - 5, 20, 7, 23, 30, 24, 9, 8, 20, 12- **Easy instruction** group times (in minutes): - 13, 6, 6, 5, 3, 6, 10, 20, 9, 12This setup examines whether the perception of task difficulty, as influenced by instructions, has a statistically significant impact on puzzle-solving times. **Independent Samples T-Test Analysis****Data Overview:**In this analysis, a dataset named "DataSet1" is used to perform a t-test, with the variable "group" divided into two subsets (1 and 2). The analysis focuses on the variable "score" with a confidence interval set at 95%.**Group Statistics:**The table below presents the group statistics based on difficulty:| Difficulty | N | Mean | Std. Deviation | Std. Error Mean ||------------|----|-------|----------------|-----------------|| Difficult | 10 | 15.800 | 8.63842 | 2.73171 || 2.00 | 10 | 9.000 | 5.01110 | 1.58465 |- **Group 1 (Difficult):** 10 samples, mean score of 15.800- **Group 2:** 10 samples, mean score of 9.000- **Standard deviations:** Group 1 (8.63842), Group 2 (5.01110)**Statistical Tests:**1. **Levene’s Test for Equality of Variances:** - F = 7.401, Sig. = 0.014 - This tests whether the variances of the two groups are equal. In this case, the p-value (0.014) indicates a significant difference in variances.2. **Independent Samples Test:** - **t-test for Equality of Means** | Assumption | t | df | Sig. (2-tailed) | Mean Difference | Std. Error Difference | 95% Confidence Interval of the Difference | |--------------------|-------|----|----------------|-----------------|-----------------------|--------------------------------------------| | Equal variances assumed | 2.153 | 18 | 0.045 | 6.800 | 3.15806 | 1.6517 to 13.43483 | | Equal variances not assumed | 2.153 | 14.441 | 0.049 | 6.800 | 3.15806 | 0.4599 to 13.55401 | - The test indicates a significant difference between the means of the two groups at a 95% confidence level under both

Equal variances: Effect size=Mean differenceStandard error difference=6.83.15806 [From the output]…

A psychologist wants to determine the effect of instructions on the time required to solve a mechanical puzzle. Each of 20 volunteers is given the same mechanical puzzle to be solved as rapidly as possible. Before the task, the subjects are randomly assigned in equal numbers to receive two different sets of

A psychologist wants to determine the effect of instructions on the time required to solve a mechanical puzzle. Each of 20 volunteers is given the same mechanical puzzle to be solved as rapidly as possible. Before the task, the subjects are randomly assigned in equal numbers to receive two different sets of

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Provide the effect size and explain the size of the effect

S1=8.64

S2=5.01

A psychologist aims to determine the effect of instructions on the time required to solve a mechanical puzzle. Twenty volunteers are tasked with solving the same puzzle as quickly as possible. Prior to starting, the subjects are randomly divided into two equal groups, each receiving different sets of instructions. One group is informed that the task is difficult, while the other is told it is easy. The time taken by each subject to solve the puzzle is recorded. The study employs a two-tailed test with a significance level of α = 0.05.

**Data**:

- **Difficult instruction** group times (in minutes):
- 5, 20, 7, 23, 30, 24, 9, 8, 20, 12

- **Easy instruction** group times (in minutes):
- 13, 6, 6, 5, 3, 6, 10, 20, 9, 12

This setup examines whether the perception of task difficulty, as influenced by instructions, has a statistically significant impact on puzzle-solving times.

**Independent Samples T-Test Analysis**

**Data Overview:**

In this analysis, a dataset named "DataSet1" is used to perform a t-test, with the variable "group" divided into two subsets (1 and 2). The analysis focuses on the variable "score" with a confidence interval set at 95%.

**Group Statistics:**

The table below presents the group statistics based on difficulty:

| Difficulty | N | Mean | Std. Deviation | Std. Error Mean |
|------------|----|-------|----------------|-----------------|
| Difficult | 10 | 15.800 | 8.63842 | 2.73171 |
| 2.00 | 10 | 9.000 | 5.01110 | 1.58465 |

- **Group 1 (Difficult):** 10 samples, mean score of 15.800
- **Group 2:** 10 samples, mean score of 9.000
- **Standard deviations:** Group 1 (8.63842), Group 2 (5.01110)

**Statistical Tests:**

1. **Levene’s Test for Equality of Variances:**

- F = 7.401, Sig. = 0.014
- This tests whether the variances of the two groups are equal. In this case, the p-value (0.014) indicates a significant difference in variances.

2. **Independent Samples Test:**

- **t-test for Equality of Means**

| Assumption | t | df | Sig. (2-tailed) | Mean Difference | Std. Error Difference | 95% Confidence Interval of the Difference |
|--------------------|-------|----|----------------|-----------------|-----------------------|--------------------------------------------|
| Equal variances assumed | 2.153 | 18 | 0.045 | 6.800 | 3.15806 | 1.6517 to 13.43483 |
| Equal variances not assumed | 2.153 | 14.441 | 0.049 | 6.800 | 3.15806 | 0.4599 to 13.55401 |

- The test indicates a significant difference between the means of the two groups at a 95% confidence level under both

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