Levels of Measurement Quiz: Nominal, Ordinal, Interval, Ratio

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Questions and Answers

In statistics, what does skewness refer to?

The square root of the average squared deviations about the mean

The nature and extent to which symmetry is present in a distribution (correct)

The division of points between the four quarters in a distribution

The measure of average variability in a distribution

What is true about Pearson's correlation coefficient when it relates two continuous variables?

It shows the strength and direction of the relationship between the variables. (correct)

It uses spearman rank-order correlation.

It is used when one variable is continuous and the other is ordinal.

It can only be between 0 and 1 inclusive.

What does the principle of least squares refer to in regression analysis?

The technique used to calculate the slope of the regression line.

The method of finding the best-fitting line through observed data points. (correct)

The process of determining the coefficient of determination.

The method of calculating standard deviation in residuals.

When comparing two independent groups using a t-test, what does having unequal variances imply?

The two groups have different variability in their scores. Signup and view all the answers

What is the purpose of a one-way ANOVA in statistical analysis?

To compare multiple independent groups. Signup and view all the answers

In a regression analysis, what does the standard error of estimate represent?

The standard deviation of the residuals around the regression line. Signup and view all the answers

When transforming a distribution to resemble a normal curve, what process involves making the distribution asymmetric?

Kurtosis Signup and view all the answers

What is the primary purpose of hypothesis testing in statistics?

To assess whether observed data support a hypothesis about a population. Signup and view all the answers

What is the critical region in hypothesis testing?

The area of extreme values that make it very unlikely to obtain results if the null hypothesis is true. Signup and view all the answers

When using a t-test for hypothesis testing, what factor determines whether equal or unequal variances should be assumed?

The result of a Levene's test Signup and view all the answers

Which level of measurement has a true zero point?

Ratio Signup and view all the answers

What type of statistics is used to provide a concise description of a collection of quantitative information?

Descriptive Statistics Signup and view all the answers

What is the property of 'moreness' in a scale?

Magnitude Signup and view all the answers

What is the purpose of post-hoc tests in ANOVA?

To determine the significance of the mean differences Signup and view all the answers

What type of scale can take on any value within a range and has an infinite number of possible values?

Continuous Scale Signup and view all the answers

What is the average of all the raw scores in a distribution?

Mean Signup and view all the answers

Study Notes

Scales of Measurement

Nominal: categorization based on one or more distinguishing characteristics, no quantitative distinctions between observations
Ordinal: involves rank ordering, no quantitative distinctions between observations
Interval: has equal intervals, no absolute zero point, used when there has an unknown or undetermined score
Ratio: has true zero point, easiest to manipulate

Measures of Central Tendency

Mode: the most frequently occurring score in the distribution
Median: the middle score of the distribution
Mean: the average of all the raw scores, affected by extreme scores
Relationship between Mode, Median, and Mean:
- Symmetrical Distribution: Mean = Median = Mode
- Positively Skewed Distribution: Mean > Median > Mode
- Negatively Skewed Distribution: Mean < Median < Mode

Measures of Variability

Range: the difference between the highest and lowest scores
Quartile: dividing points between the four quarters in the distribution
Interquartile Range: the difference between Q3 and Q1
Semi-interquartile Range: equal to the interquartile range divided by 2
Standard Deviation: a measure of variability, equal to the square root of the variance
Variance: the arithmetic mean of the squared deviations about the mean

Normal Curve

Bell-shaped, smooth, and mathematically defined curve
Highest at its center, asymptotically approaching the axis
Tails: 2-3 standard deviations above and below the mean
Stanine: a method of scaling test scores on a nine-point standard scale
Linear Transformation: retains a direct numerical relationship to the original raw score
Skewness: the nature and extent to which symmetry is absent

Standard Scores

Standard Score: a raw score that has been converted from one scale to another
Z-Scores: the results of the conversion of a raw score into a number indicating how many SD units the raw score is below or above the mean
T-Scores: a scale with a mean set at 50 and a standard deviation set at 10

Hypothesis Testing

Null Hypothesis: states there is no change, difference, or relationship
Alternative Hypothesis: states there is a change, difference, or relationship
Alpha Level or Level of Significance: the probability that the test will lead to a Type I error
Critical Region: composed of extreme values that are very unlikely to be obtained if the null hypothesis is true

Correlation and Inference

Correlation Coefficient: a number that provides an index of the strength of the relationship between two things
Types of Correlation Coefficients:
- Pearson R
- Spearman Rho
- Kendall's Coefficient
- Phi or Fourfold Coefficient
- Point-Biserial Correlation
- Rank Biserial Correlation
- Tetrachoric Correlation

Regression Analysis

Predicts the values of a dependent or response variable based on values of at least one independent or explanatory variable
Residual: the difference between an observed value of the response variable and the value of the response variable predicted from the regression line
Standard Error of Estimate: the standard deviation of the residuals in regression

Tests

T-Test (Independent): compares two groups, used when two groups are independent samples
T-Test (Dependent)/Paired Test: used when two groups are paired or matched
One-Way ANOVA: compares three or more groups, used when one IV and one DV
Two-Way ANOVA: used when two IV and one DV
Critical Value: reject the null and accept the alternative if obtained value > critical value
P-Value (Probability Value): reject null and accept alternative if p-value < alpha level

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Description

This quiz covers different levels of measurement in statistics, including nominal, ordinal, interval, and ratio scales. Topics include classification, distribution categorization, central tendency measures like mean, median, and mode, and ranking observations based on characteristics.