A school psychologist is interested in determining if children with attention deficit hyperactivity disorder (ADHD) learn better if English literature is read to them rather than having them read the material alone by themselves. A random sample of 10 sixth graders with ADHD is selected and divided into two groups of n=9. One of the groups has a story read to them (Listening Group) and the other reads the story alone by themselves (Reading Group). A test on the story is given after each group has finished reading or hearing the story. The following scores were obtained with 20 being a perfect score.what is the cohen’s d ? ### Two-Sample t-Test for Independent Groups#### Groups and Raw Data1. **Reading Group Scores:** - 10 - 10 - 7 - 12 - 8 - 8 - 10 - 9 - 112. **Listening Group Scores:** - 15 - 12 - 13 - 11 - 10 - 9 - 11 - 10 - 11#### Statistical Analysis| Statistic | Reading Group | Listening Group ||----------------|---------------|-----------------|| Count (n) | | || Mean | | || DEVSQ (SS) | | || STDEV.S | | || df | | || \( S_{(M1-M2)} \) | | || alpha | | || \( t_{crit} \) | | || \( t_{obs} \) | | || Cohen's d | | || \( r^2 \) | | |#### Decision- **Reject Ho** - **Fail to reject Ho**### Description of DataThe table presents results from a two-sample t-test comparing the means of two independent groups: a Reading Group and a Listening Group. Each group's scores on some measure are listed, and summary statistics for each group, including mean, deviation squared (DEVSQ or SS), standard deviation (STDEV.S), degrees of freedom (df), and the pooled standard error of the difference between means (\( S_{(M1-M2)} \)) are calculated.The table also displays the alpha level (the probability of a Type I error), the critical t-value (\( t_{crit} \)), the observed t-value (\( t_{obs} \)), Cohen's d (a measure of effect size), and the coefficient of determination (\( r^2 \)).The decision section indicates whether the null hypothesis (Ho) is rejected or not based on the t-test results. ### t-Test: Two-Sample Assuming Equal VariancesThis section describes the results of a t-test conducted to compare the means of two independent groups, G1 and G2, under the assumption that their variances are equal.**Group Statistics:**- **G1:** - Mean: 8.77777778 - Variance: 3.94444444 - Observations: 9- **G2:** - Mean: 11.4444444 - Variance: 3.27777778 - Observations: 9**Pooled Variance:** 3.61111111**Hypothesized Mean Difference:** 0**Degrees of Freedom (df):** 16**t-Test Calculations:**- **t Stat:** -2.97683363- **P(T<=t) one-tail:** 0.004449553- **t Critical one-tail:** 1.745883676- **P(T<=t) two-tail:** 0.008899105- **t Critical two-tail:** 2.119905299**Interpretation:**The t-test statistical outputs provide essential information to determine if there is a statistically significant difference between the means of G1 and G2. - **Mean and Variance:** Shows the central tendency and spread of the data points within each group.- **Pooled Variance:** A weighted average of the variances from both groups, used in the t-test calculation.- **Hypothesized Mean Difference:** Typically set to 0 which uses the null hypothesis that there is no difference between the means.- **Degrees of Freedom:** Reflects the number of values in the final calculation of a statistic that are free to vary.- **t Stat:** The calculated t-statistic value from the test.- **P-Values:** Indicates the probability of observing the test results under the null hypothesis. A lower value (typically less than 0.05) suggests rejecting the null hypothesis.- **Critical Values:** These are the thresholds at which the null hypothesis would be rejected for one-tail and two-tail tests, respectively.This t-test provides a detailed statistical analysis to help determine if the observed differences in group means are likely to be present in the population from which the samples were drawn.

The given data is, Reading (x) Listening(Y) 10 15 10 12 7 13 12 11 8 10 8 9 10 11…

Answered: A school psychologist is interested in…

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P