Statistics

Lecture of 1-16-07

Frequency distribution stats (arranges ALL of the scores received):

• Histograms –bar graphs of frequency distributions

• Frequency polygons –line graphs made by connecting the tops of bars and erasing the bars…

Scatter plots or scatter grams

• These are used to show a relationship or correlation.

• Make one score the ‘X’ value on a graph

• Make the second score the ‘Y’ value on a graph.

• Positive correlations have a positive slope

• Negative correlations have a negative slope

• Randomness implies no correlation

Test yourself, What is the following graph saying?

The Beta test and the SAT test are similar. People that score well on Beta also score well on SAT.

Positive correlation!

Test yourself, What is the following graph saying?

Temperature in Celsius

Dissolved Oxygen level in a river

The higher the temperature, the lower the dissolved oxygen in the river.

What is this graph saying?

Heart rate doesn’t seem to change even though the length of time it is measured changes.

What is this graph saying?

Not much. No correlation

Histogram or frequency polygon?

histogram

Histogram or frequency polygon?

Frequency polygon

Histogram or frequency polygon?

Both!

Central Tendency –statistics to find the middle o’ the bunch!

• Mode: most frequently occurring score. This is the LEAST used in statistics… just gives a quick look at the data.– 2 scores appear equally the most? ‘Bimodal’– More than 2 appear the most? ‘Multimodal!’

• Median: middle score when the data is organized by size.

• Mean: the mathematical average of a set of data. (Most preferred method of finding central tendency)

Test yourself!

Given the set: 5,6,7,7,7,8,8,9,9,10

Mode?

Median?

Mean?

7

7.5

7.6

Distributions• Normal distributions are where the data points

are in a symmetrical ‘bell shaped’ curve. This occurs when the mode, median and mean are all the same.

• Skewed distributions are when most of the data points are squeezed into one end of the curve. – When the mean is lower than the median, it is a

negative distribution.– When the mean is higher than the median, it is a

positive distribution.

Test yourself: Skewed or normal, if skewed, positive or negative?

Test yourself: Skewed or normal, if skewed, positive or negative?

Test yourself: Skewed or normal, if skewed, positive or negative?

Variability

• A measure of the distribution of scores

• 3 types: – Range (The highest score – lowest score)– Variance (A measure of how different a score is

from the mean.)– Standard Deviation (Another measure of how

different a score is from the mean.)

Facts about Variance and standard deviation:

• Standard deviation scores fall between zero and ½ the range.

• The closer a standard deviation is to zero, the closer all scores fall near the mean.

• The higher the number is, the more varied the scores.

More variability or less variability?

Scores are pretty close to the mean, and the distribution is not very wide, so there is less variability.

High Standard Deviation or Low?Low standard deviation because scores center narrowly around the mean.

Confounding Variables –When you can’t tell which variable is causing a change (in the dependant variable…)

What are the confounding variables? A soccer coach wanted to improve the team's playing ability, so he had them run two miles a day. At the same time the players decided to take vitamins. In two weeks the team was playing noticeably better, but the coach and players did not know whether it was from the running or the vitamins.

Here is another one: Ice cream consumption and murder rates are highly correlated. Now, does ice cream incite murder or does murder increase the demand for ice cream? Name some confounding variables.

How to prevent the confounds?

• Control as many variables as you can.

• Use a ‘double-blind’ experiment… one where the experimenter doesn’t know who has the treatment and who has the placebo…