BADM 2233 Exam 2

Exam 2 Study Guide

Correlation Bivariate

two variables

Correlation Range and Direction

• 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*

Weak Correlation

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

 correlation is a linear measurement and does not always equal causation

Mode

• 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

• 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

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

Leptokurtic Kurtosis

• 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?

• the sample value is equal to the mean

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

• 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)

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

• Zero

(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?

• 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