What does the F statistic in ANOVA measure a (2024)

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What does the F-statistic in ANOVA measure?a. Difference between group meansb. Variability within groupsc. Total variability in the datad. Ratio of between-group variability to within-group variabilityClear my choiceQuestion 17Not yet answeredMarked out of 4,00Flag question

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To address the question about the F-statistic in ANOVA, let's break down the components and understand what the F-statistic specifically measures.#### Solution By Steps***Step 1: Understanding ANOVA***Analysis of Variance (ANOVA) is a statistical method used to compare the means of three or more groups. It helps to determine if there are significant differences among the group means.***Step 2: Components of ANOVA***ANOVA assesses two types of variability: 1. **Between-group variability**: This measures how different the group means are from each other.2. **Within-group variability**: This measures the variability within each group, i.e., how spread out the individual data points are within their respective groups.***Step 3: The F-statistic***The F-statistic in ANOVA is calculated as the ratio of the **between-group variability** to the **within-group variability**. This statistic helps to determine if the differences between group means are significant relative to the variability within each group.#### Final AnswerThe F-statistic in ANOVA measures the **Ratio of between-group variability to within-group variability**.#### Significance and ApplicationThe F-statistic is crucial in ANOVA as it helps to infer whether the observed differences in group means are statistically significant, indicating that these differences are unlikely to have occurred by chance. This is essential in making decisions about the effects of treatments or factors in experimental designs.

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The F test statistic in a one-way ANOVA is The F test statistic in a one-way ANOVA is none of these within-groups SS/between-groups SS between-groups SS/within-groups SS between-groups MS/within-groups MS within-groups MS/between-groups MS Clear my selectionAnswered step-by-step 1 answer SEATWORK 1 Which of the following sets of data has an outlier a) 7891011 c) 7891012 b) 7891030 d) 678910 2 Which of the following measures of central tendency is appropriate for nominal variables a) Mean b) Median c) Mode d) None of these 3 Which of the following uses mean for its average a) math 10 final grades c) blood type b) internet provider d) military rank 4 Which of the following is a CORRECT statement about measures of variability a) Lower variability means individual data is lower as compared to the average of the data b) Lower variability in quiz scores means lower performance c) Lower variability means more consistent data d) Lower variability means not good result 5 It is recorded in your health card that your height falls in the 90th percentile among the Grade 10 learners What does it mean a You are taller than 90 Grade 10 learners b You are taller than 89 Grade 10 learners c You are taller than 90 of the Grade 10 learners d You are taller than 89 of the Grade 10 learnersAnswered step-by-step 1 answerA total of 50 randomized samples were assigned into 5 different treatment groups in a pharmaceutical science experiment nbspEach group includes 10 persons (subjects) nbspIn order to test if any difference is discernible among these 5 treatments one-way ANOVA was conducted for the study nbspHere are data we calculated nbspSum of square between group = 252 nbspSum of square within group = 450 nbsp SubjectTreatment1Treatment2Treatment3Treatment4Treatment512 hellip---10n =10n =10n =10n =10n =10 ANOVA Summary Table SourceSum of SquareDegree of freedomMean SquareFBetween nbsp252V1=K-1=Within450V2=N-K=Total State null hypothesis and alternative hypothesis Calculate the degree of freedom between group and the degree of freedom within group Mean squares between groups Mean squares within groups F ratio If critical value of F is 261 should we reject or accept the null hypothesis nbsp State your conclusion for this research nbspAnswered step-by-step 1 answer What does the standard deviation measure a Spread of data b Central tendency c Skewness of data d Variability of data In a perfectly symmetrical distribution the skewness isAnswered step-by-step 1 answerSolution 1No one rated this answer yet - nbspwhy not be the first nbsp To analyze the effectiveness of the three ads in influencing registered voters rsquo likelihood of voting for the candidate we will perform a one-way ANOVA (Analysis of Variance) to compare the means of the three groups The data provided in the table will be used to calculate the necessary statisticsSolution By StepsStep 1 Data CollectionCollect the data for each ad from the table Each ad has a group of registered voters who rated their likelihood of voting for the candidate on a scale of 0 to 100Step 2 Calculate Group MeansCalculate the mean likelihood of voting for the candidate for each ad group This involves summing the likelihood ratings for each group and dividing by the number of participants in each groupStep 3 Calculate Overall MeanCalculate the overall mean likelihood of voting for the candidate by summing all the likelihood ratings and dividing by the total number of participants (N = 42)Step 4 Calculate Sum of SquaresCalculate the Sum of Squares Between Groups (SSB) and the Sum of Squares Within Groups (SSW) SSB measures the variability between the group means and SSW measures the variability within each groupStep 5 Calculate Mean SquaresDivide the SSB by the degrees of freedom between groups (k - 1 where k is the number of groups) to get the Mean Square Between (MSB) Divide the SSW by the degrees of freedom within groups (N - k) to get the Mean Square Within (MSW)Step 6 Calculate F-StatisticCompute the F-statistic by dividing MSB by MSW This statistic will help determine if there is a significant difference in the means of the three groupsStep 7 Determine SignificanceUse the F-distribution table to find the critical F-value for the given degrees of freedom (between and within groups) and the desired significance level (commonly 005) Compare the calculated F-statistic with the critical F-value to determine if the differences between the group means are statistically significantFinal AnswerThe final answer will be the F-statistic and its significance level indicating whether the ads significantly influence the likelihood of voting for the candidate If the F-statistic is greater than the critical F-value the null hypothesis (that there is no difference between the group means) is rejected suggesting that at least one ad is significantly more effective than the others What is one of the factors mentioned in this scenario How many levels does it have and what are they Is it BS or WS nbsp3 ptsAnswered step-by-step 1 answer

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What does the F statistic in ANOVA measure a (2024)

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