Scientific MethodScientific Method

Statistical inference to a comparison to Statistical inference to a comparison to show the benefits to a given comparisonshow the benefits to a given comparison New plows concepts to conventional plowingNew plows concepts to conventional plowing Hay stack to hay baleHay stack to hay bale Current forestry cut down to replantingCurrent forestry cut down to replanting Storage techniques to current practicesStorage techniques to current practices

Scientific MethodScientific MethodProblem Statement or QUESTION: What do you want to

learn? How does the distance a ball falls depend on how long it has fallen?

HYPOTHESIS: The distance a ball falls is proportional to the length of time it falls. (This is a false statement, but it IS a hypothesis, it DOES make a

testable statement relating distance and time). Predict the answer to the problem. Another term for hypothesis

is 'educated guess'. This is usually stated like " If I...(do something) then...(this will occur)"

EXPERIMENT: Vary the time we allow the ball to fall.(Time is the independent variable and distance is the dependent variable).

Scientific MethodScientific MethodOBSERVE AND MEASURE: The distance ball falls during each allowed time interval.

ANALYSIS and CONCLUSIONS: Plot the distance the ball fell versus the time it fell.

INFERENCES: If this graph is linear then the hypothesis was correct and

distance is directly proportional to time. If it is NOT linear (and when we did this in class it was a

parabola), then the hypothesis is incorrect. Since the graph, (scatterplot) does not look random, but in

fact looks very much like a parabola, then there clearly IS a relationship between distance and time, but it is not a linear model.

Scientific MethodScientific Method When describing the "Scientific Method" at this point we

can ask a new question and begin the process over again. The new question would be: "If distance is not directly proportional to time of fall, then what IS the relationship between them?“

In our case, we already have enough data from the first experiment to proceed to answer this new question.

A POWER LAW fit is done to determine the functional form of the relationship between the two variables, so that a statement of the form "distance is proportional to time raised to some exponent" can be made. The power fit finds the exponent that best matches the data curve.

Scientific MethodScientific MethodSUMMARIZE RESULTS In the Free Fall lab, the results showed that the

distance was approximately equal to 1/2 the acceleration of the ball multiplied by the square of the time it fell.

Statistical InferenceStatistical Inference

Design of ExperimentsDesign of Experiments will dedicate what will dedicate what statistical inference can be completed.statistical inference can be completed. Paired Comparison (t-test)Paired Comparison (t-test) Randomized Completely (ANOVA)Randomized Completely (ANOVA) Randomized Block Design (ANOVA)Randomized Block Design (ANOVA) Covariant testsCovariant tests

Establishing your design of experiments at the Establishing your design of experiments at the first and assuring proper inference will give you first and assuring proper inference will give you insight of the data results and how they are insight of the data results and how they are presented.presented.

Tillage ExperimentTillage Experiment

3 Treatments & 3 Reps3 Treatments & 3 Reps Treatments Treatments

C – Conventional Plow SystemC – Conventional Plow System P1 – Concept of new plow #1 P1 – Concept of new plow #1 P2 – Concept of new plow #2P2 – Concept of new plow #2

Several design could be attempted Several design could be attempted

Tillage ExperimentTillage Experiment

CC P1P1 CC

P1P1 CC P2P2

P1P1 P2P2 P2P2

Tillage ExperimentTillage Experiment

P1P1

CC

P2P2

CC

P2P2

P1P1

P2P2

P1P1

CC

Tillage ExperimentTillage Experiment

CC

P1P1

CC

P2P2

P1P1

CC

CC

P2P2

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P1P1

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P2P2

About statistical analysis toolsAbout statistical analysis tools Microsoft Excel provides a set of data analysis tools— called Microsoft Excel provides a set of data analysis tools— called

the Analysis ToolPak— that you can use to save steps when the Analysis ToolPak— that you can use to save steps when you develop complex statistical or engineering analyses. You you develop complex statistical or engineering analyses. You provide the data and parameters for each analysis; the tool provide the data and parameters for each analysis; the tool uses the appropriate statistical or engineering macro uses the appropriate statistical or engineering macro functions and then displays the results in an output table. functions and then displays the results in an output table. Some tools generate charts in addition to output tables.Some tools generate charts in addition to output tables.

Related worksheet functionsRelated worksheet functions Excel provides many other Excel provides many other statistical, financial, and engineering worksheet functions. statistical, financial, and engineering worksheet functions. Some of the statistical functions are built-in and others Some of the statistical functions are built-in and others become available when you install the Analysis ToolPak.become available when you install the Analysis ToolPak.

Accessing the data analysis toolsAccessing the data analysis tools The Analysis ToolPak The Analysis ToolPak includes the tools described below. To access these tools, includes the tools described below. To access these tools, click click Data AnalysisData Analysis on the on the ToolsTools menu. If the menu. If the Data Data AnalysisAnalysis command is not available, you need to load the command is not available, you need to load the Analysis ToolPak Analysis ToolPak add-inadd-in program. program.

ANOVA statistical analysis toolsANOVA statistical analysis tools

The Anova analysis tools provide The Anova analysis tools provide different types of variance analysis. different types of variance analysis. The tool to use depends on the The tool to use depends on the number of factors and the number of number of factors and the number of samples you have from the samples you have from the populations you want to test.populations you want to test.

ANOVA: Single FactorANOVA: Single Factor ANOVA: Two-Factor With ANOVA: Two-Factor With

ReplicationReplication ANOVA: Two-Factor Without ANOVA: Two-Factor Without

ReplicationReplication

T-test statistical toolsT-test statistical toolsThe The Two-Sample t-TestTwo-Sample t-Test analysis tools test for analysis tools test for equality of the population means underlying each equality of the population means underlying each sample. The three tools employ different sample. The three tools employ different assumptions: that the population variances are assumptions: that the population variances are equal, that the population variances are not equal, that the population variances are not equal, and that the two samples represent before equal, and that the two samples represent before treatment and after treatment observations on treatment and after treatment observations on the same subjects.the same subjects.

t-Test: Two-Sample Assuming Equal t-Test: Two-Sample Assuming Equal Variances Variances

t-Test: Two-Sample Assuming Unequal t-Test: Two-Sample Assuming Unequal VariancesVariances

t-Test: Paired Two Sample For Meanst-Test: Paired Two Sample For Means

Z-test statistical toolsZ-test statistical toolsThe z-Test: Two Sample for Means analysis The z-Test: Two Sample for Means analysis tool performs a two-sample z-test for tool performs a two-sample z-test for means with known variances. This tool is means with known variances. This tool is used to test the null hypothesis that there used to test the null hypothesis that there is no difference between two population is no difference between two population means against either one-sided or two-means against either one-sided or two-sided alternative hypotheses . If variances sided alternative hypotheses . If variances are not known, the worksheet function, are not known, the worksheet function, ZTEST, should be used instead.ZTEST, should be used instead.

Correlation statistical toolsCorrelation statistical tools The CORREL and PEARSON worksheet functions both The CORREL and PEARSON worksheet functions both

calculate the correlation coefficient between two calculate the correlation coefficient between two measurement variables when measurements on each measurement variables when measurements on each variable are observed for each of N subjects. (Any missing variable are observed for each of N subjects. (Any missing observation for any subject causes that subject to be ignored observation for any subject causes that subject to be ignored in the analysis.) The Correlation analysis tool is particularly in the analysis.) The Correlation analysis tool is particularly useful when there are more than two measurement variables useful when there are more than two measurement variables for each of N subjects. It provides an output table, a for each of N subjects. It provides an output table, a correlation matrix, showing the value of CORREL (or correlation matrix, showing the value of CORREL (or PEARSON) applied to each possible pair of measurement PEARSON) applied to each possible pair of measurement variables.variables.

You can use the correlation analysis tool to examine each You can use the correlation analysis tool to examine each pair of measurement variables to determine whether the two pair of measurement variables to determine whether the two measurement variables tend to move together— that is, measurement variables tend to move together— that is, whether large values of one variable tend to be associated whether large values of one variable tend to be associated with large values of the other (positive correlation), whether with large values of the other (positive correlation), whether small values of one variable tend to be associated with large small values of one variable tend to be associated with large values of the other (negative correlation), or whether values values of the other (negative correlation), or whether values of both variables tend to be unrelated (correlation near zero).of both variables tend to be unrelated (correlation near zero).

Histogram statistical toolsHistogram statistical tools The Histogram analysis tool calculates The Histogram analysis tool calculates

individual and cumulative frequencies for a individual and cumulative frequencies for a cell range of data and data bins. This tool cell range of data and data bins. This tool generates data for the number of generates data for the number of occurrences of a value in a data set.occurrences of a value in a data set.

For example, in a class of 20 students, you For example, in a class of 20 students, you could determine the distribution of scores in could determine the distribution of scores in letter-grade categories. A histogram table letter-grade categories. A histogram table presents the letter-grade boundaries and the presents the letter-grade boundaries and the number of scores between the lowest bound number of scores between the lowest bound and the current bound. The single most-and the current bound. The single most-frequent score is the mode of the data.frequent score is the mode of the data.

F-Test statistical analysisF-Test statistical analysis F-Test Two-Sample for VariancesF-Test Two-Sample for Variances The F-Test Two-Sample for Variances analysis tool performs a The F-Test Two-Sample for Variances analysis tool performs a

two-sample F-test to compare two population variances.two-sample F-test to compare two population variances. For example, you can use the F-test tool on samples of times in For example, you can use the F-test tool on samples of times in

a swim meet for each of two teams. The tool provides the result a swim meet for each of two teams. The tool provides the result of a test of the null hypothesis that these two samples come of a test of the null hypothesis that these two samples come from distributions with equal variances against the alternative from distributions with equal variances against the alternative that the variances are not equal in the underlying distributions.that the variances are not equal in the underlying distributions.

The tool calculates the value f of an F-statistic (or F-ratio). A The tool calculates the value f of an F-statistic (or F-ratio). A value of f close to 1 provides evidence that the underlying value of f close to 1 provides evidence that the underlying population variances are equal. In the output table, if f < 1 “P(F population variances are equal. In the output table, if f < 1 “P(F <= f) one-tail” gives the probability of observing a value of the <= f) one-tail” gives the probability of observing a value of the F-statistic less than f when population variances are equal and F-statistic less than f when population variances are equal and “F Critical one-tail” gives the critical value less than 1 for the “F Critical one-tail” gives the critical value less than 1 for the chosen significance level, Alpha. If f > 1, “P(F <= f) one-tail” chosen significance level, Alpha. If f > 1, “P(F <= f) one-tail” gives the probability of observing a value of the F-statistic gives the probability of observing a value of the F-statistic greater than f when population variances are equal and “F greater than f when population variances are equal and “F Critical one-tail” gives the critical value greater than 1 for Alpha.Critical one-tail” gives the critical value greater than 1 for Alpha.

Random # statistical toolsRandom # statistical toolsThe Random Number Generation analysis The Random Number Generation analysis tool fills a range with independent random tool fills a range with independent random numbers drawn from one of several numbers drawn from one of several distributions. You can characterize distributions. You can characterize subjects in a population with a probability subjects in a population with a probability distribution.distribution.

For example, you might use a normal For example, you might use a normal distribution to characterize the population distribution to characterize the population of individuals' heights, or you might use a of individuals' heights, or you might use a Bernoulli distribution of two possible Bernoulli distribution of two possible outcomes to characterize the population of outcomes to characterize the population of coin-flip results.coin-flip results.

Other statistical toolsOther statistical toolsRank and PercentileRank and Percentile

The Rank and Percentile analysis tool produces a table that The Rank and Percentile analysis tool produces a table that contains the ordinal and percentage rank of each value in a contains the ordinal and percentage rank of each value in a data set. You can analyze the relative standing of values in a data set. You can analyze the relative standing of values in a data set. data set. RegressionRegression

The Regression analysis tool performs linear regression The Regression analysis tool performs linear regression analysis by using the "least squares" method to fit a line analysis by using the "least squares" method to fit a line through a set of observations. You can analyze how a single through a set of observations. You can analyze how a single dependent variable is affected by the values of one or more dependent variable is affected by the values of one or more independent variables.independent variables.SamplingSampling

The Sampling analysis tool creates a sample from a The Sampling analysis tool creates a sample from a population by treating the input range as a population. When population by treating the input range as a population. When the population is too large to process or chart, you can use a the population is too large to process or chart, you can use a representative sample. You can also create a sample that representative sample. You can also create a sample that contains only values from a particular part of a cycle if you contains only values from a particular part of a cycle if you believe that the input data is periodic.believe that the input data is periodic.

Dr. Grisso - BobbyDr. Grisso - Bobby

I will be leaving next Thursday 11/2 @ noonI will be leaving next Thursday 11/2 @ noon I will be on-site all day 10-26I will be on-site all day 10-26 I have meeting with Dr. Brahne Friday morning I have meeting with Dr. Brahne Friday morning

(tomorrow) from 8:30 – 10 am(tomorrow) from 8:30 – 10 am I have meeting with the AMAREW boss on I have meeting with the AMAREW boss on

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Dr. Grisso - BobbyDr. Grisso - Bobby

I will back on 1/10/07 until I will back on 1/10/07 until 2/8/07 (30 days) 2/8/07 (30 days)

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