Read the following paragraph and answer the questions that follow : A researcher has data (sample n = 500) on eight personality variables i.e. Activity, Sociability, Talkativeness, Warmth, Anxiety, Worry, Anger, and Depression. The correlation matrix was evaluated for factorability by Bartlett’s Test of Sphericity (p < .001) and KMO = .86. The eigenvalues were 3.2, 2.4, 0.54, 0.42, 0.41, 0.39, 0.37 and 0.27. She used principal component analysis instead of PAF. Using Guttman and Scree criteria retained factors. The varimax and promax rotations were used.
Bartlett’s Test of Sphericity results indicate that correlation matrix of :
population is not identity matrix.
Bartlett's test of sphericity (Bartlett, 1950) checks whether the variables are intercorrelated enough to justify factor analysis. Its null hypothesis is that the population correlation matrix is an identity matrix, i.e. all correlations among the variables in the population are zero and the variables are unrelated.
Like all inferential tests, it uses the sample correlation matrix to draw a conclusion about the population. Here p < .001, so the null hypothesis is rejected: the population correlation matrix is not an identity matrix, and there are real correlations that can be factored.
Statements about the sample matrix are not what the test concludes: the sample matrix is known directly, and with sampling error it will almost never be exactly an identity matrix. Concluding that the population matrix is an identity matrix would correspond to a non-significant result, which is not the case here.
Hence, the answer is population is not identity matrix.
Similar Questions
If a frequency distribution has some extreme scores, then appropriate measure of variability will be .........
Identify the correct sequence of the following activities associated with research data :
(i) Data collection
(ii) Construction of frequency tables
(iii) Cleaning of data
(iv) Presentation of data in charts.
Codes :
Which of the following is a correct about assumption of homogeneity of variance in t-test ?
In a standardized regression analysis, the value of intercept is :
The PCA shall :
What is the percentage of variance first unrotated PCA shall explain ?
Which of the following is correct about KMO value ?
How many factors can be retained for rotation using Guttman and Scree criteria ?
The varimax rotation shall result in :
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Important Questions from Data Analysis - Teaching
Given below are two statements:
Statement I: In two tail test, 2.5% of the area of the normal curve falls on the right of 1.96 standard deviations above the mean and 2.5% to the left of 1.96 standard deviations below the mean.
Statement II: In one tail test, for testing the difference between large sample means, a z score of 1.64 is taken as Yardstick at the 5% level of significance.
In light of the above statements, choose the most appropriate answer from the options given below:
In a traditional extract–transform–load (ETL) workflow, data scrubbing performed during the transformation stage is:
Temperature (°C) Number of stations 0–10 1 10–20 2 20–30 3 30–40 4 40–50 5 50–60 4 60–70 3 70–80 2 80–90 1 Using the standard grouped-data interpolation formula with position 3N/4, estimate the third quartile Q₃ of the temperature distribution.
Temperature (°C) Number of stations 0–10 1 10–20 2 20–30 3 30–40 4 40–50 5 50–60 4 60–70 3 70–80 2 80–90 1 Using class midpoints, what is the estimated arithmetic mean temperature?
Temperature (°C) Number of stations 0–10 1 10–20 2 20–30 3 30–40 4 40–50 5 50–60 4 60–70 3 70–80 2 80–90 1 Using the standard grouped-data interpolation formula, what is the estimated median temperature?
