Descriptive Statistics (Exam 1)

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Characteristics of Normally Distributed Data (5)

-Unimodal -Symmetrical (no skew) -Bell Shaped (no kurtosis) -Asymptotic (tails never = 0) -Mean, median, mode are centered *normality testing is always a precursor to any analysis

Significant Kurtosis?

if K is greater than 2x the SEK, hen kurtosis is significant and distribution is likely not normal

Leptokurtic

positive skew, peak is higher and narrower than normal (think "leap" = high)

Skew/Kurtosis

shape of the spread (variability); distribution

Use Median When...

there are extreme scores

Weighted Mean

(bc mean is sensitive to outliers) used to restore balance to over or underrepresented segments of a sample

Ways to Examine Variability

Range Standard Deviation Standard Error Variance

Mode

most frequently occurring score

Calculating Skew

skewness = 3(Mean -Median) / Standard Deviation (-) value = (-) skew (+) value = (+) skew 0 = normal distribution

Elements of Variability

spread dispersion

Variance

another common measure of spread in a data set found in many statistical calculations *formula is s^2 (standard deviation without the square root

Standard Deviation

average distance of each observation from the mean (average amount of variability) most frequently reported measure of variability

Central Tendency

central/typical value around which data clusters (mean, median, mode)

Standard Error (Variance)

combines information from the standard deviation to tell you how confident you are about your population mean estimate; used to assign confidence intervals to our population mean estimate

Use Mode When...

data are categorical

Significant Skew?

if skew is greater than 2x the standard error of skew, then skew is significant and distribution is likely not normal

Variability

measure of how much scores differ from the mean

Kurtosis

measure of how peaked or flat the distribution curve will be

Skewness

measure of whether and how much extremes are affecting the bell curve (normal distributions)

Platykurtic

negative skew, peak is lower and wider than normal (think "plat" = flat)

Positive Skew

the mean is bigger than the median -"slide" runs in positive direction & "bumb" is pulled to the left of the normal curve

Negative Skew

the mean is smaller than the median -"slide" runs in a negative direction & "bumb" is pulled to the right of the normal curve

Systematic Variability

type of variability that has been identified as causes of variability

Error

type of variability that has not been or can not be accounted for

Descriptive Statistics

used to describe data sets used to visualize data 1st step in any statistical analysis

1st Quartile (Q1)

value at which 25% of all observations fall below

Median

value at which 50% of all scores fall below, and 50% fall above

3rd Quartile (Q3)

value at which 75% of all observations fall below

No Mode

when no values occur more than once

Bimodal Distribution

when two values occur the same number of times

Standard Deviation vs. Variance

-S.D. is in the same unites, making it ideal to describe data -variance is often a required input for statistical tests

Calculating Mode

-list all values in a distribution -tally the number of times each value occurs -value occurring the most is the mode

Range

-most general estimate of variability -most course estimate as well b/c only 2 extreme scores are used -conclusions should never be based on variability alone -very important in predictive statistics

Calculating the Median

-rank order from lowest to highest -find "middle" score, or average middles scores if sample size is even

Percentiles (Uses)

-used to get a feel for how spread out the data is and where most of the observations are contained -also as a comparison score (provides "normalized referenced" measure to compare one value to the larger sample)

Inter-Quartile Tange (IQR)

=Q3-Q1 the larger the IQR, the more variable the data is


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