Statistics Pha 6300 Exam 2

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Variables falling in a certain interval on which no theoretical restrictions are placed. Measured along a scale

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Continuous Variables - examples height, BP, time, age, distance, temperature, annual snowfall amount, weight, improvement in SAT score, GPA

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These types of variables have a restriction placed on them. There is no continuity

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Discrete - Gender/sex, schooling level, day of the week, hair color, SAT prep program, Class (P1...), race, ethnicity, college major, eye color, blood type, battery manufacturer

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These types of variables assumes a value of one if a criterion is met, a value of zero otherwise

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Dummy

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The number of observations in a given statistical category

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Absolute Frequency

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The ratio of the absolute frequency to the total # of data points in a frequency distribution

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Relative Frequency ex: Class with freq of 6 within a sample size 38
relative frequency = 6/38 x100 = 15.8%

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How many #'s are in each class (category)

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Simple Frequency

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It's conducted by adding the frequency of scores in any class interval to the frequencies of all the class intervals below it on the scale of measurement

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Cumulative Frequency Distribution (it tells how many values are in that interval and all intervals less than it.

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Distributions points toward the low scores

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Negatively skewed distribution

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Distributions with a tail pointing toward high values of a variable are

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positively skewed

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Degree of peakedness, the extent to which, for a given standard deviation, observations cluster around a central point

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Kurtosis

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A degree of kurtosis that is elongated and flat

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Platykurtic (flatter)

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A degree of kurtosis that appears taller and narrow

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Leptokurtic (taller)

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A degree of kurtosis that tends to be bell-shaped like the normal curve

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Mesokurtic - a perfect mesokurtic curve is also called a normal curve

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Used to illustrate the relationship between 2 variables when the scale of measurement of the independent variable is nominal. Measurements are discrete (there's no continuity). For qualitative variables

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Bar graph

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They're used to display the sizes of parts that make up a whole, used commonly for qualitative data.
It's a circle graph divided into pieces, each displaying the size of some RELATED piece of information

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Pie Chart

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Type of bar graph that illustrates the frequencies of individuals scores or scores in class intervals by the length of its bar. The intervals are on the x-axis (range of scores), Y-axis = frequency of scores

The bars are continuous, shape depends on the choice of the sixe of the intervals

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Histogram (no space between bars)

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A graphical display of a frequency table, intervals are shown on the X-axis, # of scores in each interval is represented by the height of a point located above the middle of the interval, points are connected so that together with the X-axis

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Frequency Polygon

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Graph that illustrated the relationship between 2 quantitative variables; both measured on either an interval or a ratio scale

Shows how much one variable is affected by another

Relationship between 2 variables is called their correlation

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Scatter Plot/Scattergram - positive = / negative = \

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Summarizes how 2 pieces of information are related and how they vary depending on one another

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Line Graph

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The numbers along a side of the line graph are called

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the scale

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Provides a simple graphical summary of a set of data

Shows the median, the range and inter-quartile range skewness and potential outliers

Useful when comparing 2 or more sets of data

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Box Plot (Box and whisker diagrams)

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It's a graph of the cumulative frequencies (or cumulative % frequencies) against the class upper boundaries

To determine the various %ile points in a distribution of scores

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Ogive

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This measure of location or central tendency should not be used when there are extreme values (ouliers) in the data set

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Mean or Average - add all the values and divide by the # of values

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This measure of location or central tendency is not affected by outliers

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Median - arrange #'s in order and the median is the number in the middle or the average of the two #'s in middle

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In a normal distribution this measure of location or central tendency coincides with the values of the mean and the median

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Mode - most frequently occurring value in the set of scores

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The spread or variability of the scores around their average in a single sample

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Standard deviation (s) - mathematically the square root of the variance

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The standard deviation of the the sampling distribution

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Standard Error (of the mean) = se

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Also called the standard normal curve or standard normal distribution
mean = 0
standard deviation = 1
variation = 1
The curve is symmetric and symptomatic

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z distribution

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If the area representing the desired proportion falls on both sides of the mean, do we add or subtract the two area segments?

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ADD

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If the desired area falls between two z scores on the same side of the mean, do we add or subtract to find the proportion?

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SUBTRACT

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Formula to transform your raw values into z scores =

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_
z = (x - x ) / s
_
x = mean
x = raw score
s = standard deviation

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Family of symmetrical, bell-shaped distributions that change as the sample size changes

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Students t distributions
there's a specific t distribution for every sample of a given size

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Mean = 0
Symmetrical
Variance greater than 1
Range: - infinity to + infinity
Shape: less peaked in the center and higher tails than the normal distribution

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t - distributions

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The __ distribution for infinite degrees of freedom is identical to the normal distribution

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t

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We reject a true Ho - when it is falsely concluded that a significant difference exists between the groups being studied

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Type I Error (alpha) = 1 - probability value (the probability of making type I error)

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When we fail to reject a falso Ho - when it is falsely concluded that no significant difference exists between populations, when in fact a true difference exists

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Type II Error = beta

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degrees of freedom of the column

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K-1 (K=number of groups/levels)

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degrees of freedom of the row

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N-K

N=total sample size
K = number of groups/sizes

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Skewed to the right
Only positive numbers (begins at 0)
One-tailed test
Ratio of variability

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F-distributions

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Equation of Mean Squares (Variance) Between (Factor)

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MSB = SSB / (K-1)

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Equation of Mean Squares Variance Within (Error)

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MSW = SSW / (N-K)

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F Statistic =

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MSB / MSW (must always be positive)

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If the calculated F value is > or = to the table value:

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REJECT Ho

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If the calculated F value is < than the table value:

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FAIL TO REJECT Ho

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is sometimes referred to as the omnibus

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F-test used in Anova