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Central Tendency, Variability, Z-Scores - Coggle Diagram
Central Tendency
Central Tendency is the score that displays and defines the center of a distribution. Central tendency tries to identify the "average" individual.
Central Tendency uses the large amount of data and crunch them down to a value that is representative of them all.
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The purpose of central tendency is to find the one value that represents the distribution. Generally the mean is thought to be the best measure.
There are situations when median is a better for measuring central tendency: skewed distribution/extreme scores.
Mode is used as an alternative to mean when measures are on an nominal scale, discrete values, and when describing shape.
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Variability
Provides a quantitative measure of the differences between scores in a distribution and describes the degree to which the scores are spread out or clustered together.
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unbiased- A statistic that, on average, provides an accurate estimate of the corresponding population parameter. The sample mean and sample variance are unbiased statistics.
The goal of inferential statistics is to use the limited information from samples to draw general conclusions about populations.
Range
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For a continuous variable the range is the difference between the upper limit for the highest score and the lower limit for the lower score.
The problem with range is that it can found using two scores that are extreme and not representative of the scores in the distribution.
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Standard Deviation
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Standard deviation uses the mean as a reference point and measures the distance between each score and the mean.
standard deviation provides a measure of the standard, or average, distance from the mean, and describes whether the scores are clustered closely around the mean or are widely scattered.
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Inferential Statistics
the goal of inferential statistics is to detect meaningful and significant patterns in research results
Variability plays an important role in the inferential process because the variability in the data influences how easy it is to see patterns
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Z-Scores
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statistical technique that uses the mean and the standard deviation to transform each score (X value) into a z-score or a standard score
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scores alone don't always provide all the information needed to determine their position in a distribution
original, unchanged scores that are the direct result of measurement are called raw scores
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z-scores consist of 2 part a positive or negative sign and a magnitude. These parts are required to describe where a raw score is located in a distribution.
Z-Scores and locations
The (+/-) sign of a z-score tells a researcher whether the score is located above (+) or below (-) the mean.
The numerical value shares the difference between the score and the mean in the terms of number of standard deviations.
+1.00 corresponds to a position exactly 1 standard deviation above the mean; -1.00 corresponds to a position exactly 1 standard deviation below the mean.
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Z-Score Forumla
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- The formula for calculating Z-scores is X minus the mean divided by the standard deviation. The first step is to subtract the mean from the data point that you would like to examine.
- Divide the subtracted value by the standard deviation.
Other relationships between x, standard deviation, mean, and z-scores
z-score establishes a relationship between the score, mean, and standard deviation
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Z-Scores for comparisons
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Before you can begin to make comparisons, you must know the values for the mean and standard deviation for each distribution.
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