Success Criteria: I will be able to analyze data about my classmates. We need cans! Warm –Up: Get a computer and log in. Date Title Page # 8/15 Analyzing Classmate Data – Once Again #

Go to Ms. Steensen’s website (it is linked from the Gateway Homepage under academicsscienceMs. Steensen) Click on the announcement titled Google Doc - Data About Our Class. Download the Excel document and save it under your login.

Data Description We want to start by describing the data. We describe data by doing “summary statistics” and answering: What is the central/typical value? What is the spread around that value?

Central / Typical Value Type of Analysis What this Analysis Means Formula for Calculation How to calculate in Excel Result for my data Mean (we use this a lot!) This is the average value Add all of the data and divide by the number of data points. Go to the formula box and type = AVERAGE (highlight the data) Median (we do not use this a lot!) This is the midpoint of the data. Arrange data smallest to largest then locate the middle piece of data. (Note: If there are an even number of data points, average the 2 center points. Go to the formula box and type = MEDIAN (highlight the data)

Spread Range (we do not use this a lot!) Type of Analysis What this Analysis Means Formula for Calculation How to calculate in Excel Result for my data Range (we do not use this a lot!) This is the total spread of the data. Subtract the smallest value from the largest value. Go to the formula box and type = MAX(highlight the data) – MIN (highlight the data)

Success Criteria: I will be able to analyze data about my classmates. We need cans! Warm –Up: Get a computer and log in. Date Title Page # 8/16 Analyzing Classmate Data – Once Again #

Statistics Test Wednesday, August 21 there will be a test over statistics. The types of questions that you completed for homework under “practice questions” will be similar to those you see on the test. There will also be one “practical” question where you will use Excel to calculate some statistics on a data set (you may use notes)

What this Analysis Means Spread – Standard Deviation Type of Analysis What this Analysis Means Standard Deviation(we use this a LOT!) This is the standard measure of spread – it calculates the average distance of the data from the mean. Sx = Σx2 - (Σx)2 n n - 1 Where: Sx is the standard deviation of sample Σ stands for ‘sum of’ x stands for the individual measurements in the sample n is the number of individuals in the sample You can calculate standard deviation using the formula:

About 68% of values are within 1 standard deviation of the mean! Spread – Standard Deviation About 68% of values are within 1 standard deviation of the mean!

In This Class - We Will Assume Normal Distribution

How to calculate in Excel Spread – Standard Deviation How to calculate in Excel The easiest way is to calculate Sx stepwise and use Excel like a calculator. Copy your data into a new column. Create a column for squared values. In the formula bar type =(highlight individual data)^2. Copy that down the column. Calculate Σ by typing =SUM (highlight the data) in a new row. Plug each value into the formula below. Sx = Σx2 - (Σx)2 n n - 1 Where: Sx is the standard deviation of sample Σ stands for ‘sum of’ x stands for the individual measurements in the sample n is the number of individuals in the sample

Practice with Data Description Calculate the descriptive data statistics for your group’s data. Write the statistics for your group in your notebook and take notes on the process of calculating/determining each statistic. Don’t forget to save your excel document under your student folder or e-mail it to yourself.

Asking and Answering Questions with Data We collect data to investigate natural phenomena, observe patterns, and answer questions. Statistics plays a key role in being able to use data effectively to answer questions. Ask a question using your data. (i.e. Are males or females older in our class?) [IV = gender DV = age]

Copy and separate your data based on the question you are asking. Calculate the mean and standard deviation of both groups of data. Determine the n (sample size) of both groups of data. Create one graph showing the mean of both groups of data (in this case we will create a bar graph, though line graphs will be what we use most of the time!!) Add error bars.

Spread Error Bars (use this a lot!) Type of Analysis What this Analysis Means Formula for Calculation How to calculate in Excel Error Bars (use this a lot!) A graphical representation of the variability of the data. The STANDARD DEVIATION. Click under Chart Tools  Layout Error Bars More Error Bar Options  Custom  [Positive/ Negative Error Value = standard deviations separated by a comma]

This error bar shows the values within 1 standard deviation. Error bars can show a variety of types of “spread stats.” so you must always label the error bars as +/- 1 standard deviation! Error Bars

Answering Questions With Statistics In order to tell if the difference between two sets of data is significant, the t-test is commonly used. A t-test works by comparing the standard deviations of two data sets and giving a number to how much they overlap. The more the standard deviations overlap, the less likely the difference is significant – this is also shown in error bars

The T-Test Terms Term Definition How to Calculate Degrees of Freedom The number of values in the final calculation of a statistic that are free to vary. Sum of sample sizes of each group -2 t Values Statistical description of how much 2 data sets overlap Probability (p) The statistical probability that chance alone could produce the difference. 0.05 (5%) and lower are SIGNIFICANT! Use a table of t-values. i.e. page 7 in the textbook. Many t-test calculators will give you a p value.

Calculating the T-test Excel is challenging to use as a t-test calculator. Go to studentsttest.com Enter your data Click “groups have unequal variance” and “2- Tailed t-test” Click calculate The page will give you a p value – if the p value is less than 0.05, then your groups are statistically different!!!

What does my t-test mean? P = 0.54796 Males are NOT older than females. What does my t-test mean?

Data Analysis Section in Labs Levels/marks Aspect 1 Aspect 2 Aspect 3 Recording raw data Processing raw data Presenting processed data Complete/2 Records appropriate quantitative and associated qualitative raw data, including units and uncertainties where relevant. Processes the quantitative raw data correctly. Presents processed data appropriately and, where relevant, includes errors and uncertainties. You must describe what statistics you use, what those statistics mean, and how you can calculate them (include a sample calculation!) Include error bars and uncertainties on all graphs!

Example Data Analysis Section Are female or male students older in 4th period science class? The average age for females was 16.39 years +/- 0.04 years. The mean was calculated by adding the ages of all female students and dividing by the number of female students in the class. The mean describes the central/typical value for the data set. For example, 16.25+16.58+17.50+… / 13 = 16.39 The standard deviation for females was 0.409. The standard deviation is a measure of spread in the data set. The formula for standard deviation is …… For example, the numbers in this data set were…… Example Data Analysis Section

Reflecting What are the purposes of statistics? What statistics will I need to use often in my own experimentation? Why?