16 Questions
In statistics, what does skewness refer to?
The nature and extent to which symmetry is present 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.
What does the principle of least squares refer to in regression analysis?
The method of finding the best-fitting line through observed data points.
When comparing two independent groups using a t-test, what does having unequal variances imply?
The two groups have different variability in their scores.
What is the purpose of a one-way ANOVA in statistical analysis?
To compare multiple independent groups.
In a regression analysis, what does the standard error of estimate represent?
The standard deviation of the residuals around the regression line.
When transforming a distribution to resemble a normal curve, what process involves making the distribution asymmetric?
Kurtosis
What is the primary purpose of hypothesis testing in statistics?
To assess whether observed data support a hypothesis about a population.
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.
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
Which level of measurement has a true zero point?
Ratio
What type of statistics is used to provide a concise description of a collection of quantitative information?
Descriptive Statistics
What is the property of 'moreness' in a scale?
Magnitude
What is the purpose of post-hoc tests in ANOVA?
To determine the significance of the mean differences
What type of scale can take on any value within a range and has an infinite number of possible values?
Continuous Scale
What is the average of all the raw scores in a distribution?
Mean
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
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.
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