Statistics

Recording the results from our studies.

Descriptive Statistics

• Just describes sets of data.

• You might create a frequency distribution.

• Frequency polygons or histograms.

Measures of Central Tendency• Mode – score that occurs most often

EX: 3,5,5,7,5,4,9,6,8,7,10 5 is the mode

• Median – score in the halfway point EX: 3,4,5,5,5,6,7,7,8,9,10 6 is the median

• Mean – average score EX: 3+5+5+7+5+4+9+6+8+7+10=69

69/11 6.27 is the mean

Mean, Median, Mode

• The weekly salaries of six employees at McDonalds are $140, $220, $90, $180, $140, $200.

– For these six salaries, find: •(a) the mean •(b) the median •(c) the mode

Mean, Median, Mode• AnswersMean: 90+ 140+ 140+ 180 + 200 + 220 =$ 161.67

6

Median: 90,140,140,180,200,220

The two numbers that fall in the middle need to be averaged.

140 + 180 = 160

2

Mode: 90,140,140,180,200,220

The number that appears the most is 140

Let’s say you are looking to move to a new place….

• The average income of a family in the new city is 70,000 – not too bad….

• However….• 26 families make less than 70,000• Only 3 families make more than

70,000

Skewed Distributions

15 20 25 30 35 40 45 50 90 475 710

70

Mode Median Mean

One Family Income per family in thousands of dollars

Distributions• Outliers skew

distributions.• If group has one

high score, the curve has a positive skew (contains more low scores)

• If a group has a low outlier, the curve has a negative skew (contains more high scores)

Measures of Variation

Measures of Variability• Range: distance

from highest to lowest scores.

• Standard Deviation: the variance of scores around the mean.

• The higher the variance or SD, the more spread out the distribution is.

• Do scientists want a big or small SD?

Calculating the Standard Deviation

1. Figure out the Mean: 16 4 = 42. Take mean & figure out difference

from each point: 2-4=-2, 2-4=-2, 4-4=0, 8-4=4

3. Square each difference:4,4,0,164. Add together: 4+4+0+16=245. Divide by #: 24 4 = 6 This is

the variance6. Take square root: 2.45

Data: 2,2,4,8

Normal Distribution

• In a normal distribution, the mean, median and mode are all the same.

Normal Distribution

A standard deviation of 15 accounts for about 68% of responses.

A normal distribution is a bell shaped curve.

Statistical Significance

• How likely it is that an obtained result occurred by chance

• Odds must be less than 5% (p<.05) in order for results to be statistically significant

• This means that your results are 95% (p>.95) a result of your IV