BADM 2233 Exam 2

Exam 2 Study Guide

Correlation Bivariate

two variables

Correlation Range and Direction

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* Range is from -1.00 to 1.00
* Scores closer to 1 or -1 are stronger, while scores closer to zero are waker


* positive (+) correlations /, negative (-) correlations \\, no correlation \*random dots everywhere\*

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Weak Correlation

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0.00 to 0.35 or -0.35

Moderate Correlation

0.36 to 0.65 or -0.36 to -0.65

Strong Correlation

0\.66 or -0.66 and higher

Linear Relationship

the data is best described as a straight line

Curvilinear Relationship

the trend in the data changes directions

Heterogeneity

* “A samples diversity”

Homogeneity

* “how similar are the cases?”

Common Variance

* a measure of area
* is correlation squared

Correlation and Causation

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 correlation is a linear measurement and does not always equal causation

Mode

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*  the most frequent score in a distribution
* may not be equal values on each side of the mode
* may have multiple modes (bimodal, trimodal, etc.)

Median

* center point in a distribution
* 50th percentile
* average of the two middle scores (even observations)
* median is the middle score (odd observations)
* is a measure of relative position, not always even distances on both sides

Mean

* arithmetic average of a distribution
* most likely to fluctuate forms sample to sample
* most statistics use this value
* differences with values that balance on each side

Symmetrical Skew (Mesokurtic)

* no skew
* mean is in the middle
* between -0.5 and 0.5

Positive Skew

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* mean is to the right of the median
* value is higher than 1
* Curve is at the left

Negative Skew

* mean is to the left of the median
* value is less than -1
* Curve is at the right

Highly Skewed

* If skewness is less than -1 or greater than 1

Moderately Skewed

* If skewness is between -1 and -0.5 or between 0.5 and 1

Symmetric Skew (Mesokurtic)

* If skewness is between -0.5 and 0.5

Kurtosis

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* how bunched up scores are within the middle of the distribution

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Leptokurtic Kurtosis

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* scores are bunched up toward the center of the distribution
* value is greater than 2.0

Platykurtic Kurtosis

* fewer scores in the middle of the distribution and more variation
* value is less than -2.0

Statistical Dispersion

* means the extent to which numerical data is likely to vary about an average value.

Range

* distance from highest to lowest
* least stable/useful
* highest minus lowest

Variance

* average squared distance from the mean
* measures variability from the average

Standard Deviation

* square root of the variance
* cannot be negative
* used to measure dispersion around mean of data set
* shows variation from average
* is sensitive to outliers

The Normal Distribution

* Gaussian distribution
* x-axis: scores
* y-axis: frequency
* is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Z-Scores

* A raw score’s distance from the mean
* expressed in standard deviation units

Negative z-Score

* means the value is below the mean

Positive z-Score

* means the value is above the mean

What does it mean when the z-Score is = 0?

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* the sample value is equal to the mean

(T/F)The Pearson correlation is good for evaluating curvilinear relationships.

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* False, It draws a line straight through the data (line of best fit) not good for a curvilinear graph (only appropriate for linear).

When we observe a great variety of outcomes in out observations, we have what?

* Heterogeneity

What is represented on the y-axis of the normal curve?

* Frequency

How is the standard deviation calculated?

* square root of the variance

Interpret the correlation r = -0.50

* moderate negative relationship

What percentage of values would we expect above a z-score of 0.0?

* 50% (\*mean\* we expect 50% above 50% below)

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The sum of deviations from the mean will always equal what value?

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* Zero

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(T/F) We can have a negative variance value.

* False because the variance is the average SQUARED.

Based on the normal distribution. What percentage of students will score below the mean?

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* 50%, 50% will score better than the mean and 50% will score higher than the mean.

A gaussian curve is another name for what?

* Normal distribution, Gauss came up with normal distribution.

The most frequently occurring observation is called what?

* The mode

Interpret 0.95

* a strong positive correlation (Closer to 0 the weaker the relationship, the closer to -1, or 1 the stronger the relationship)

What do we call the center point of the Distribution?

* the median

The difference between the smallest and largest values is…

* range

Which z-Score is likely an outlier -0.50, 2.37, 1.00, -1.20

* 2.37, larger z-Scores are likely outliers

The entire curve of normal distribution represents what percentage?

* 100%

Is it possible to have negative z-scores?

* yes

What does dispersion represent?

* how spread out the data is

What data typically lies on the x-axis?

* scores