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Questions and Answers

What is the primary purpose of a scatter plot in analyzing bivariate data?

To calculate the mean of the two variables

To determine the correlation coefficient between the two variables

To visually represent the relationship between the two variables (correct)

To test the normality of the data

Which of the following is a requirement for using the Pearson product-moment correlation?

Both variables must be normally distributed (correct)

Both variables must have the same unit of measurement

Both variables must be linearly related

Both variables must have the same range of values

What does a straight diagonal line in a Q-Q probability plot indicate?

The data is correlated

The data is linearly related

The data is not normally distributed

The data is normally distributed (correct)

What is the term used to describe the degree of the relationship between linearly related variables?

Correlation coefficient Signup and view all the answers

Which of the following methods can be used to determine if the data is following a normal distribution?

All of the above Signup and view all the answers

What is the purpose of testing the normality of the data in correlation analysis?

To ensure the validity of the Pearson product-moment correlation Signup and view all the answers

What can be concluded from the Q-Q plots of age and height?

The data in age and height are normal. Signup and view all the answers

What is the Pearson correlation coefficient (r) between the toddler's age in months and their height?

r = 0.75 Signup and view all the answers

What is the interpretation of the correlation coefficient (r = 0.75)?

There is a high positive correlation. Signup and view all the answers

What statistical test is used to test if there is a significant relationship between two sets of scores?

T-test Signup and view all the answers

What is the purpose of normality testing in this context?

To ensure the data meets the assumptions of the statistical test. Signup and view all the answers

What can be concluded from the p-values (0.749 and 0.231) in the normality testing?

The data is normal. Signup and view all the answers

What does a P-value greater than the alpha indicate in a normality test?

The data are normal Signup and view all the answers

What is the interpretation of a correlation coefficient of ±0.75?

High correlation Signup and view all the answers

What is the purpose of the Shapiro-Wilk Test?

To test for normality assumption diagnostics Signup and view all the answers

What does a correlation coefficient of ±0.25 indicate?

Slight correlation Signup and view all the answers

What is the null hypothesis in a normality test?

The sample data does not follow a normal distribution Signup and view all the answers

What is the purpose of the Pearson Product-Moment Correlation?

To determine the strength of a correlation Signup and view all the answers

Study Notes

Normality Tests

The Q-Q plot can be used to determine if data is normally distributed, where points lying on a diagonal line indicate normality.
The Shapiro-Wilk test is a numerical method for testing normality, where a p-value greater than 0.05 indicates normality and a p-value less than 0.05 indicates non-normality.

Correlation Analysis

The Pearson Product-Moment Correlation coefficient (r) measures the degree of linear relationship between two variables.
The correlation coefficient (r) can be interpreted as:
- 0.00: no correlation
- ±0.01 to ±0.20: very low correlation
- ±0.21 to ±0.40: slight correlation
- ±0.41 to ±0.70: moderate correlation
- ±0.71 to ±0.90: high correlation
- ±0.91 to ±0.99: very high correlation
- ±1.00: perfect correlation
A scatter plot is a visual representation of the relationship between two variables, showing direction and strength of the relationship.

Hypothesis Testing

Null hypothesis (Ho): the data does not follow a normal distribution
Alternative hypothesis (Ha): the data follows a normal distribution
Alpha (α) is the level of significance, typically set at 0.05

Example Problem

Determine if there is a significant relationship between toddlers' age and height
Use the Pearson Product-Moment Correlation formula to calculate the correlation coefficient (r)

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