descriptive statistics

Median

Midpoint Adv: used for sets of data that have an outlier Outliers do not impact the median as they do the mean (Ex: billionaire's wealth wouldn't influence median)

standard deviation

Most commonly used measure of variability

Outliers are visible on

graphs & data analysis outputs

A positively skewed distribution

has extreme scores at the higher end of the distribution.

A negatively skewed distribution

has extreme scores at the lower end of the distribution.

Calculation of variance shows

how far each score is from the mean

percentile ranks

indicate the percentage of scores that fall at or below a given score

Always report the

mean

3 measures of central tendency

mean, median, mode

Why would it be helpful to find out percentages in addition to the frequency?

Easier to visualize (fraction/percentages of whole) Serves as a "standard metric" to compare groups of different sizes

A t-score is used when sample size is less than

30

A score that represents the mean has a z-score of

0

Two Main Types of measures of relative position

1. Percentile ranks 2. standard scores

Mean

Arithmetic average of a set of scores Best for sets of data that do NOT have an outlier(s) extreme scores Becomes skewed (shifted) because of outlier/extreme scores Ex: a city's mean income will be influenced by a billionaire Advantages: useful when comparing sets of data Disadvantages: affected by extreme values (outliers)

descriptive statistics

Can calculate statistics by hand or use assistance of statistical programs Excel, SPSS, and many other programs exist Will explore SPSS in ED600 You're NOT responsible for any equations or doing statistics by hand Should just be able to understand the concepts behind the statistics

Types of descriptive statistics

Frequencies Measures of central tendency Measures of variability/dispersion Measures of relative position Measures of relationship

Measures of Relationship

Indicate degree to which two sets of scores are related

Measures of Relative Position

Indicate where a score falls in the distribution relative to all other scores

Measures of Variability

Provide an index of the degree of spread in a distribution of scores

3 types of measures of variability

Range Variance Standard deviation

Mode

The value that gets repeated most Extreme values do not impact mode Not as popular or useful as mean and median

Normal Distribution

When large amount of data gathered bell-shaped and symmetrical Fifty percent of the scores are above the mean and 50% are below the mean The mean, median, and mode have the same value Most scores are near the mean

Express different scores on a common scale

allows for norm-referenced scoring and reporting of individual's scores

Variance:

amount of spread among scores

Range:

difference between the highest and lowest score

Pearson r takes into account score

every

Standard Deviation (SD):

measure of how spread out numbers (for a group as a whole) are around the mean compared to the norm

If you have major outliers report

median & explain about outlier(s)

Smaller standard deviations indicate data is

more concentrated around the mean

Larger standard deviations indicate

more dispersion

Skewness

not symmetrical Mean, median, and mode are not same value

Frequency:

refers to the number of times something occurs

Pearson r is the most stable measure of

relationship

A standard score

reports how many standard deviations a given score is from the mean of a distribution

Kurtosis

shape of distribution normal Peaked flat

When a distribution is not normally distributed, it is said to be

skewed

Pearson r is

statistic used to calculate relationship for interval or ratio data

A z-score (most common standard score) is directly tied to

the standard deviation