STEM Fair Graphs & Statistical Analysis

• Objectives:– Today I will be able to:

• Construct an appropriate graph for my STEM fair data• Evaluate the statistical significance of my data using the appropriate

statistical test

• Informal Assessment – students questions and responses to STEM Fair Discussions

• Formal Assessment – STEM fair data collection and analysis rubric

• Common Core Connection – Value Evidence– Use technology and digital media strategically and capably

Lesson Sequence

• Evaluate: Warm-Up• Explain: Pass out STEM Fair Checklist• Explain: Pass out STEM Fair Data Collection

and Analysis Rubric• Explain/ Evaluate: Review Data,Graphing and

Statistics Expectations• Evaluate: Exit Ticket

Warm - Up

• Convert the speed of 60 miles/ hour to meters/second.

Note (): – 1 mile = 5280 feet– 3.28 feet = 1 meter

Objectives

• Today I will be able to:– Construct an appropriate graph for my STEM fair

data– Evaluate the statistical significance of my data

using the appropriate statistical test

Homework

• Study for the Lab Equipment and Safety Quiz tomorrow

• Work on STEM fair Data Analysis Section

Agenda

• Warm-Up• Pass out STEM Fair Checklist• Pass out STEM Fair Data Collection and

Analysis Rubric• Review Data,Graphing and Statistics

Expectations• Exit Ticket

Pass out STEM Fair Checklist and 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 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

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

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 Analysis1. Data collection & input2. Data summary & reduction3. Data analysis: Perform statistical test(s) and draw

conclusion

Drill

• What is an independent variable?

• What is a dependent variable

• What is a control?

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.

Sadly, Bar Graphs May be Used

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

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-TestsThis 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).

• Most of you will be doing this type of test!

Chi-Square TestThis 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 (we can never accept the

alternative 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

Discuss with a partner

• What type of statistical test should I use to analyze my data?

STEM Fair Data Collection and Analysis Due: September 27

• Mr. Klotz’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?