The analysis in Table 10–12 is from a hypothetical study comparing performance of children with communication disorders, their chronological age-matched peers, and their communication age-matched peers. The study had two independent variables: a group variable that was nonexperimental and a method variable that was experimental. The information reported includes descriptive statistics for the three groups of children across the two methods. The inferential data analysis was a two-way analysis of variance (ANOVA) with group and method as the independent variables. First, examine the descriptive statistics. What do you think might have happened in this study? You might consider entering the means in a spreadsheet and generating a bar graph or line graph. ### Hypothetical Study: Comparing Performance of Children with Communication Disorders#### Descriptive StatisticsThis section displays the mean (M), standard deviation (SD), and sample size (n) for children in three different groups: Children with Communication Disorders (CD), Chronologically-Aged Matched (Chron-Matched), and Communication-Age Matched (Comm-Matched). Results are presented for both a new teaching method and an old teaching method.- **New Method:** - **Children with CD:** M = 54.00, SD = 2.28, n = 6 - **Chron-Matched:** M = 49.33, SD = 2.16, n = 6 - **Comm-Matched:** M = 51.33, SD = 2.28, n = 6- **Old Method:** - **Children with CD:** M = 45.92, SD = 2.20, n = 6 - **Chron-Matched:** M = 51.17, SD = 2.14, n = 6 - **Comm-Matched:** M = 47.41, SD = 2.24, n = 6#### Analysis of Variance (ANOVA)The ANOVA table assesses the effects of the different teaching methods and group categorizations on performance outcomes. - **Source of Variation:** - **Group:** df = 2, Sums of Squares = 6.51, Mean Square = 3.26, F-ratio = 0.52, Probability = 0.60 - **Method:** df = 1, Sums of Squares = 88.67, Mean Square = 88.67, F-ratio = 14.07, Probability = 0.0008 - **Group by Method Interaction:** df = 2, Sums of Squares = 140.51, Mean Square = 70.26, F-ratio = 11.15, Probability = 0.0002 - **Error:** df = 30, Sums of Squares = 189.04, Mean Square = 6.30 - **Total:** df = 35, Sums of Squares = 424.74Interpretation of this data suggests significant effects of the teaching method and interaction between group and method on performance

Descriptive statistics: The mean and standard deviation of children with CD using new method are…

Answered: Table 10-12. Hypothetical Study…

MATLAB: An Introduction with Applications

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Author:Amos Gilat

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The analysis in Table 10–12 is from a hypothetical study comparing performance of children with communication disorders, their chronological age-matched peers, and their communication age-matched peers. The study had two independent variables: a group variable that was nonexperimental and a method variable that was experimental. The information reported includes descriptive statistics for the three groups of children across the two methods. The inferential data analysis was a two-way analysis of variance (ANOVA) with group and method as the independent variables. First, examine the descriptive statistics. What do you think might have happened in this study? You might consider entering the means in a spreadsheet and generating a bar graph or line graph.

### Hypothetical Study: Comparing Performance of Children with Communication Disorders

#### Descriptive Statistics

This section displays the mean (M), standard deviation (SD), and sample size (n) for children in three different groups: Children with Communication Disorders (CD), Chronologically-Aged Matched (Chron-Matched), and Communication-Age Matched (Comm-Matched). Results are presented for both a new teaching method and an old teaching method.

- **New Method:**
- **Children with CD:** M = 54.00, SD = 2.28, n = 6
- **Chron-Matched:** M = 49.33, SD = 2.16, n = 6
- **Comm-Matched:** M = 51.33, SD = 2.28, n = 6

- **Old Method:**
- **Children with CD:** M = 45.92, SD = 2.20, n = 6
- **Chron-Matched:** M = 51.17, SD = 2.14, n = 6
- **Comm-Matched:** M = 47.41, SD = 2.24, n = 6

#### Analysis of Variance (ANOVA)

The ANOVA table assesses the effects of the different teaching methods and group categorizations on performance outcomes.

- **Source of Variation:**
- **Group:** df = 2, Sums of Squares = 6.51, Mean Square = 3.26, F-ratio = 0.52, Probability = 0.60
- **Method:** df = 1, Sums of Squares = 88.67, Mean Square = 88.67, F-ratio = 14.07, Probability = 0.0008
- **Group by Method Interaction:** df = 2, Sums of Squares = 140.51, Mean Square = 70.26, F-ratio = 11.15, Probability = 0.0002
- **Error:** df = 30, Sums of Squares = 189.04, Mean Square = 6.30
- **Total:** df = 35, Sums of Squares = 424.74

Interpretation of this data suggests significant effects of the teaching method and interaction between group and method on performance

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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