Podcast
Questions and Answers
Many inference tests used in analyzing experiments have sampling distributions that become normally distributed with increasing ______.
Many inference tests used in analyzing experiments have sampling distributions that become normally distributed with increasing ______.
sample size
A normal curve is important in the behavioral sciences because many of the variables measured have distributions that closely approximate the ______.
A normal curve is important in the behavioral sciences because many of the variables measured have distributions that closely approximate the ______.
normal curve
In a normal distribution, an equal number of scores are above and below the ______, making it a symmetrical distribution.
In a normal distribution, an equal number of scores are above and below the ______, making it a symmetrical distribution.
midpoint
The normal curve approaches the horizontal axis and gets closer, but never quite touches it; thus, the curve is said to be ______ to the horizontal axis.
The normal curve approaches the horizontal axis and gets closer, but never quite touches it; thus, the curve is said to be ______ to the horizontal axis.
Approximately two-thirds of the scores lie within one ______ of the mean in a normal distribution.
Approximately two-thirds of the scores lie within one ______ of the mean in a normal distribution.
In a normal distribution, scores that fall more than two standard deviations from the mean are considered relatively ______.
In a normal distribution, scores that fall more than two standard deviations from the mean are considered relatively ______.
Tests with very little variability among the raw scores have small standard ______.
Tests with very little variability among the raw scores have small standard ______.
When raw scores are converted to standard scores, the scores are said to be ______.
When raw scores are converted to standard scores, the scores are said to be ______.
The purpose of standard scores is to ______ individual raw scores into a standard form for better comparison and interpretation.
The purpose of standard scores is to ______ individual raw scores into a standard form for better comparison and interpretation.
[Blank] scores can be calculated for distributions of any shape, not just normally shaped distributions.
[Blank] scores can be calculated for distributions of any shape, not just normally shaped distributions.
The mean of the ______ scores always equals zero, simplifying comparisons and analyses.
The mean of the ______ scores always equals zero, simplifying comparisons and analyses.
The ______ deviation of z scores is always equal to 1, making it easier to compare different distributions.
The ______ deviation of z scores is always equal to 1, making it easier to compare different distributions.
To find the area given a raw score, one must first draw a curve showing the population and locate the relevant area by entering the score on the ______ axis.
To find the area given a raw score, one must first draw a curve showing the population and locate the relevant area by entering the score on the ______ axis.
After finding the z score, one must look up its equivalent on the table to determine the ______ between the mean and z.
After finding the z score, one must look up its equivalent on the table to determine the ______ between the mean and z.
To convert the proportion to a percentage, multiply it by ______.
To convert the proportion to a percentage, multiply it by ______.
When determining the raw scores that divide a distribution, one must identify the area ______ the specified percentage.
When determining the raw scores that divide a distribution, one must identify the area ______ the specified percentage.
In the context of finding a raw score that divides a distribution, if 70% of the scores lie below a certain raw score, then ______% must lie above it.
In the context of finding a raw score that divides a distribution, if 70% of the scores lie below a certain raw score, then ______% must lie above it.
When finding a missing raw score, one must substitute the relevant values into the ______ equation and solve for X.
When finding a missing raw score, one must substitute the relevant values into the ______ equation and solve for X.
Transforming raw scores into their corresponding z scores does not change the shape of the ______.
Transforming raw scores into their corresponding z scores does not change the shape of the ______.
If a test has a mean of 80 and a standard deviation of 12, then a score a distance of 1 standard deviation above the mean can be calculated with the equation $(μ + 1σ) = \frac{(μ + 1σ) - μ}{σ} = ______$
If a test has a mean of 80 and a standard deviation of 12, then a score a distance of 1 standard deviation above the mean can be calculated with the equation $(μ + 1σ) = \frac{(μ + 1σ) - μ}{σ} = ______$
Flashcards
Why is the normal curve important?
Why is the normal curve important?
A curve where many variables' distributions closely approximate it, inference tests become normally distributed with larger sample sizes, and many inference tests require normally distributed sampling distributions.
Normal Curve
Normal Curve
A theoretical distribution of population scores with a bell shape, symmetry, and mean, median, and mode at the same point.
Asymptotic
Asymptotic
The curve approaches the horizontal axis but never touches it.
Scores in a Normal Curve
Scores in a Normal Curve
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Variability and Standard Deviation
Variability and Standard Deviation
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Purpose of Standard Scores
Purpose of Standard Scores
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Z-Scores
Z-Scores
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Z-score Transformation
Z-score Transformation
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Shape of Z-score Distribution
Shape of Z-score Distribution
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Mean of Z-Scores
Mean of Z-Scores
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Z-Score Standard Deviation
Z-Score Standard Deviation
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Finding Area from Raw Score Steps
Finding Area from Raw Score Steps
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Finding Raw Score from Area
Finding Raw Score from Area
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Standard Score Conversion Formula
Standard Score Conversion Formula
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Study Notes
- The normal curve is crucial in behavioral sciences.
Importance of the Normal Curve
- Many measured variables closely approximate a normal distribution, like height, weight, intelligence, and achievement.
- Inference tests in experiment analysis have sampling distributions that become normally distributed as sample size increases, such as the Sign test and Mann-Whitney U test.
- Some inference tests depend on normally distributed sampling distributions like the z-test, Student’s t-test, and F test.
Properties of the Normal Curve
- It's a theoretical distribution of population scores.
- It takes the shape of a symmetrical distribution described by a specific equation.
- Symmetry is a key feature where an equal number of scores falls above and below the midpoint.
- The mean, median, and mode coincide at the same point in a symmetrical distribution.
- Two inflection points exist on either side of the mean, marking where the curvature changes direction.
- The inflection points are at least one standard deviation away from the mean.
- The curve approaches the horizontal axis without ever touching it, described as asymptotic to the horizontal axis.
Normal Curve Application
- Psycho-educational measurements often assume a normal distribution.
- School psychologists find the normal curve concept especially important.
- Approximately 68.26% of scores lie within one standard deviation of the mean.
- 95% of scores fall within two standard deviations of the mean.
- Over 99% of scores are within three standard deviations of the mean.
- Scores beyond two standard deviations from the mean are relatively rare and considered clinically significant.
Standard Deviation Recap
- Understanding the standard deviation of a test's raw scores is essential before standardizing the scores.
- Tests with minimal variability among raw scores have small standard deviations.
- Tests with high variability among raw scores have large standard deviations.
- The standard deviation is the square root of the variance in the raw scores distribution.
- Converting raw scores to standard scores results in "standardized" scores.
- Standard scores transform individual raw scores into a standard form, offering a more descriptive perspective of scores within the distribution, utilizing Z-scores, IQ scores, T-scores, and scaled scores.
Z Scores
- Z scores are standard scores with a mean of 0 and a standard deviation of 1.
- They serve as "golden scores".
- An IQ of 130 lacks meaning without a reference group for comparison.
- Scores are transformed to make them meaningful.
- For example, an IQ of 130, which is two standard deviations above the mean, corresponds to 47.72% of scores between the mean and that point, positioning the IQ score above approximately 97.72% of the population.
- Z scores are transformed scores indicating how many standard deviations a raw score is from the mean.
- They are calculated using formulas, with different equations for population and sample data.
- Score transformation is the process of altering the raw score.
Characteristics of Z Scores
- Z scores maintain the same shape as the original set of raw scores.
- Transforming raw scores into z scores alters the score values but doesn't change the distribution shape or relative positions.
- Z scores are not always normally shaped and can be calculated for distributions of any shape.
- The mean of all z scores in a distribution always equals zero.
- Raw scores at the mean have a z value of zero.
- The standard deviation of z scores is always equal to 1.
Finding Area Given Score
- Draw a diagram showing the population, and indicate the relevant score and requested area.
- Shade the area desired.
- Convert raw score into Z score
- Find the area between the mean and z on the Z table
- Convert proportion to a percentage by multiplying by 100
Finding Score Given Area
- This process determines raw scores from a distribution of aptitude scores.
- It's the reverse of finding areas given raw scores.
- When given what percentage of the scores lie below a raw score, find the opposite percentage to find the area to search for in Z table
- Find the area in the Z table or closest to that area
- Insert the Z score into the transformation formula and equate to X
Other Scale Conversions
- Other scale conversions include deviation IQs, scaled scores, stanines, and SAT scores.
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