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How do we make sense of data?

Physics is an experimental science in which we make measurements and try to make sense of the data taken. Because of natural variations in the phenomenon and because of the measurements techniques, the numbers we collect generally vary. We will need to make conclusions by looking at an ensemble of data points. To do so we look at patterns and we use statistics.

In this class, we will not assume any prior knowledge of statistics and we will not require detailed statistical calculations. Instead we will focus on knowing a few important concepts and we will focus on using statistical tools to visualize and compute for us all the important properties of our dataset.

In this class we will primarily use StatKey. StatKey which is a free Javascript application that is used with the textbook "Statistics: Unlocking the Power of Data".

To enter data into Statkey, you will need

• you need to create a .csv (comma separated value) file with a first row of header (a "txt" file can also work). For most, using excel may be the easiest. You can save any data in excel in .csv format using the "save as" option.
• We will then upload the file in StatKey.

In lab 4 we will use the "two quantitative variable statistics".

Type of variables

• Independent variable: This is the one changed by the scientist.
• Dependent variable: This is the variable that the scientist observes to see if or how it is affected by changes made in the independent variable.
• Controlled variable. This is a variable that the scientist will try to keep constant while changing the independent variable.

In your lab this week you will study how current (measured by angle on compass) depends on the length of the wire.  In this case, we can label our variable types as:

• Independent variable: length of the wire
• Dependent variable: angle
• Controlled variable: type of wire (and diameter), batteries

There are often multiple control variables. It really refers to anything that you are NOT changing.

Two quantitative variables.

We will often look at cases where we have two quantitative (numerical) variables. We will use the scatterplot to visualize.

When we look at a scatterplot, we are interested to see whether there is a pattern, a trend.

For example, the image below shows a scatterplot created in Statkey of the ph vs average mercury for 53 different lakes in Florida.

While the data is pretty scattered, a careful observation of this scatterplot reveals there there seems to be a trend in that high ph lakes seems to be low average mercury while the reverse is true of low ph.

On the right of the image, you see the mean and standard deviation of each variable as well as the sample size. There is also a new statistics we have not seen before called the correlation.

The correlation often denoted r is a number between -1 and 1. Values close to +1 or -1 means strong association (positive or negative) while values close to 0 means no association.