+ Data Analysis Chemistry GT 9/18/14

+ Drill The crown that King Hiero of Syracuse gave to Archimedes to analyze had a volume of 575 mL and a mass of 6.8 kg. Was it pure gold? What was it mostly (do you think)? HW: Work on your data analysis

+ Objectives: IWBAT: Calculate density, given mass, volume, or density Construct an appropriate graph for my STEM fair data Evaluate the statistical significance of my data using the appropriate statistical test

+ HW Review Let’s put up some density problems on the board. Any Qs about activity? Pass ‘em in.

+ Pass out STEM Fair Checklist, Data Collection and Analysis Rubric

+ Data

+ Data Tables Make sure the data tables include: – A title – Appropriate labels and SI units for both the dependent and independent variables – Averages of data Your graphs should be a representation of the averages (means) of your data! Not all the data that you collect!

+ Graphs

+ What type of graph should I use to analyze my data?

+ Types of graphs Pie Chart – Used to compare parts to a whole (percentages) Bar Graph – compare values in a category or between categories. Multiple bar graphs compare relationships of closely related data sets. These graphs may be used to demonstrate relationships in non-continuous data or data intervals. DO NOT use for your STEM project

+ Types of Graphs Continued Time-Series Plot – dependent variable is numerical and the independent variable is time XY Line Graph – dependent and independent variables when both are numerical and the dependent variable is a function of the independent variable Scatter plot – Shows how two variables MAY be related to one another

+ Why do I need error bars on my graph?

+ Error bars Show variability in data Indicate error and/or uncertainty in measurement A larger size error bar means the measurement/ data collected is not as accurate Error bars should be one standard deviation in length

+ What is standard deviation?

+ Standard Deviation Determines validity of data set for each testing group If data points are close to the average, there is a small standard deviation and the data is valid If the standard deviation is large, the data points are not close to the average and the validity of the data is questioned Calculate using Excel

+ What is the coefficient of correlation (r)?

+ Coefficient of Correlation (r) used to fit a straight line (best-fit) to sample data to summarize the relationship between x and y values. Sample correlation coefficient (r) is calculated to measure the extent to which x and y are linearly related. Example would be looking at the relationship between % salinity in water (x) and nitrate level (y). Example of results would be that a simple linear regression model explained 91.3% of total variation in nitrate level by relating it to salinity

+ Coefficient of Correlation (r) Only use if graph is a line graph or scatterplot (not for time series) Describes the direction and strength of 2 sets of variables Calculate when the line of best fit is made on a graph in excel R Values – Positive Correlation = Direct relationship for data – Negative correlation = Indirect relationship for data – r = 0, no correlation – r < 0.5, weak correlation – r > 0.8, strong correlation – r = 1 perfect correlation

+ Coefficient of Correlation examples

+ Graphing Checklist Discuss with a partner: What type of graph is being used to analyze the data? Is this graph the correct choice? Are error bars used? Can my scatterplot have a line of best fit? Should a coefficient of correlation be calculated?

+ STEM Fair: Statistical Analysis

+ Summary Statistics Mean – represents population mean (calculated same as the average) Standard Deviation – shows the variability of an observation in a sample

+ Summary Statistics Cont. Confidence Interval - the width of the interval shows how precisely the value of the mean is known Shows the degree of confidence that our mean is between two values typically a 95% CI is used

+ Steps to Completing Statistical Analysis 1. Data collection & input 2. Data summary & reduction 3. Data analysis: Perform statistical test(s) and draw conclusion

+ Test Assumptions Most statistical tests have assumptions that should be met such as: Data follows a normal population distribution & Large enough sample size to detect change. We are ignoring statistical test assumptions for this project.

+ Types of Statistical Tests Paired T-Test Unpaired T-Test ANOVA Chi-Square Coefficient of Correlation

+ T-Tests This test is used to compare the data from two different testing groups to determine if they are significantly different. There are two different types: PAIRED: Used when the data consist of pairs of observations on the same person or object. Example: comparing the heart rate of individuals before and after watching a scary movie. UNPAIRED: Used when the data from one group are not directly linked to the data of the other group. Example: comparing the effect of red light versus blue light on the growth of plants.

+ ANOVA This test is used to determine whether there are any significant differences between the means of three or more independent (unrelated) groups. Example: determining whether exam performance differed based on test anxiety levels amongst students. Students are divided into three independent groups (e.g., low, medium and high-stressed students).

+ Chi-Square Test This test is used to determine if there are differences between two or more frequency distributions. Both independent and dependent variables need to be categorical data. Example: comparing the foraging height (upper, middle, and lower) of yellow warblers in different tree species (oak, maple, aspen, and hazel).

+ Analyzing the Test Results Two possible conclusions after carrying out a test Reject Hypothesis Fail to reject Hypothesis

+ Analyzing the Test Results (cont.) P-values – one way to report the result of an analysis is by saying whether or not the hypothesis was rejected at a specified level of significance (we will use.05) The smaller the calculated p-value, the greater the difference between the groups. Example: the difference in means from our testing groups is statistically significant at the.05

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+ Discuss with a partner What type of statistical test should I use to analyze my data?

+ STEM Fair Data Collection and Analysis Due: October 10 Ms. Bloedorn’s Expectations: Data Tables Appropriate Graphs Complete Statistical Analysis Worksheet and Place in the Folder

+ Exit Ticket What questions do you have about the Data Collection and Analysis Section?