statistics. descriptive statistics organize & summarize data (ex: central tendency &...

Statistics

Descriptive Statistics

• Organize & summarize data (ex: central tendency & variability

Scales of Measurement

Nominal• Categories for

classifying• Least informative scaleEX: divide class based on

eye color

Ordinal• Order of relative

position of items according to some criterion

• Tells order but nothing about distance between items

Ex: Horse race

Scales of Measurement

Interval • Scale with equal

distance btw pts but w/o a true zero

• Ex: Thermometer

Ratio• Scale with equal

distances btw the points w/ a true zero

• Ex: measuring snowfall

Frequency Distribution

Histogram & Frequency Polygon

• X axis- possible scores• Y axis- frequency

Normal Curve of Distribution

• Bell-shaped curve• Absolutely symmetrical• Central Tendency:

mode, mean, median?

Central Tendency• Mean, Median and Mode.• Watch out for extreme scores or outliers.

$25,000-Pam $25,000- Kevin$25,000- Angela$100,000- Andy$100,000- Dwight$200,000- Jim$300,000- Michael

Let’s look at the salaries of the employees at Dunder Mifflen Paper in Scranton:

The median salary looks good at $100,000.The mean salary also looks good at about $110,000.But the mode salary is only $25,000.Maybe not the best place to work.Then again living in Scranton is kind of cheap.

Skewed Distributions

Positively Skewed Negatively Skewed

Bimodal Distribution

• Each hump indicates a mode; the mean and the median may be the same.

• Ex: Survey of salaries- Might find most people checked the box for both $25,000-$35,000 AND $50,000-$60,000

Variability

• On a range of scores how much do the scores tend to vary or depart from the mean

• Ex: golf scores of erratic golfer or consistent golfer

Standard Deviation• Statistical measure of variability in a group of

scores• A single # that tells how the scores in a

frequency distribution are dispersed around the mean

Normal Distribution

Standard Deviation

1212121212

20 22021 22122 22223 223

Correlation

DOES NOT IMPLY CAUSATION!

Correlation: Two variable are related to each other with no causation

• The strength of the correlation is defined with a statistic called the correlation coefficient (+1.00 to -1.00)

• Positive- Indicates the two variables go in the same direction

• EX: High school & GPA

CorrelationPositive• two variables go in the

same direction• EX: High school & GPA

Negative• two variable that go in

the opposite directions• EX: Absences & Exam

scores

Graphing Correlations- Scatter Plot

No Correlation- Illusory

Strength of the Correlation ( r)

• Correlation Coefficent- Numerical index of the degree of relationship between two variable or the strength of the relationship.

• Coefficient near zero = no relationship between the variables ( one variable shows no consistent relationship to the other 50%)

• Perfect correlation of +/- 1.00 rarely ever seen• Positive or negative ONLY indicate the direction,

NOT the strength

Coefficient of Determination-Index of correlation’s predictive power

• Percentage of variation in one variable that can be predicted based on the other variable

• To get this number, multiply the correlation coefficient by itself

• EX: A correlation of .70 yields a coefficient of determination of .49 (.70 X .70= .49) indicating that variable X can account for 49% of the variation in variable Y

• Coefficient of determination goes up as the strength of a correlation increases (B.11)

Inferential Statistics

• The purpose is to discover whether the finding can be applied to the larger population from which the sample was collected.

• P-value= .05 for statistical significance.

• 5% likely the results are due to chance.

Null Hypothesis

• Is the observed correlation large enough to support our hypothesis or might a correlation of the size have occurred by chance?

• Do our result REJECT the null hypothesis?

Statistical Significance

• It is said to exist when the probability that the observed findings are due to chance is very low, usually less than 5 chances in 100 (p value = .05 or less)

• When we reject our null hypothesis we conclude that our results were statistically significant.

Type I v. Type II Error

• Type I Error- said IV had an effect but it didn’t– False alarm

• Type II Error- don’t believe the IV had an effect but it really does

• Which is worse?