1.1 Statistical Analysis

Learning Goals: Basic Statistics Data is best demonstrated visually in a graph form with clearly labeled axes and a concise title. Independent variables (the treatment or manipulated variable) resides on the X axis. The dependent variable (the response that is measured) resides on the Y axis. Statistical results are clearly demonstrated by a summation table and/or graphically. Analytical statistics provide confidence in rejecting or accepting a null hypothesis.

Graphs are easier to observe the trends in the data and results can be visually determined by the observer.

Data Table showing sales and profits. Which of the following is true for this data set? A: As sales increase, the profits always increase B: As sales increase, some of the profits increase C: There is no clear relationship between sales and profits D: As sales increase, some of the profits decrease.

Bar graph which allows for easy comparisons between data sets. Which of the following is true for this data set? A: As sales increase, the profits always increase B: As sales increase, some of the profits increase C: There is no clear relationship between sales and profits D: As sales increase, some of the profits decrease.

Line graph which allows for easy observations of trends..

Visual diplays of data must contain all the following:

Descriptive and analytical statistics are tools to help researchers gain understanding from the data they gather. Descriptive statistics describe the characteristics of the data: the mean or average, the variance, the standard deviation, the mode, the median, the shape of the data (skewness or kurtosis), and N: the number of observations.

1.1.2 Calculate the mean and standard deviation of a set of values When analyzing data, it is important to know both the means and the standard deviation mean formula mean A. colubris – 15.9 mean C. Latirostris – 18.8

1.1.2 Calculate the mean and standard deviation of a set of values Standard deviation formula

Histograms allow for sorting and observing the distibution of the data.

What kind of graph is this? A: Histogram B: Trend Line Graph C: Bar Graph D: Pie Chart

What is the average weight? A: About 48 kilos B: 49 kilos C: 50 kilos D: Cannot tell from the data given

How many items were weighed? A: 150 B: 49.7 C: 65 D: Cannot be determined.

What is this type of distibution of data called? A: Skewed B: Block C: Normal D: Chi Squared

Normal distribution, graph of standard deviation around the mean, mu.

Explain how the standard deviation is useful for comparing the means and the spread of data between two or more samples A small value of standard deviation indicates that the data is not spread, and very close to the mean value (more reliable) A large value indicates a wider spread of data (perhaps, less reliable)

Analytical statistics allow conclusions to be drawn from the data: Comparisons of means using the standard error statistic gives confidence to accepting or rejecting the null hypothesis.

1.1.1 State that error bars are a graphical representation of the variability of data all measurements are subject to error so it is important to show this by using error bars error bars can be used for both variables (x and y axis) csupomona.edu

Calculation of the standard error aka confidence limits aka +/- range of the mean What happens to the quality of the estimate of the mean (standard error) as the sample size increases? A: SE gets larger B: SE gets smaller C: SE does not change D: Cannot tell from this equation SE: Standard error of the mean s : standard deviation n : number of observations

Calculation of the standard error aka confidence limits aka +/- range of the mean What happens to the quality of the estimate of the mean (standard error) if the standard deviation is very large? A: SE is large. B: SE is small. C: SE does not change D: Cannot tell from this equation SE: Standard error of the mean s : standard deviation n : number of observations

Controlled experiments manipulate the variable that is predicted to cause differences between groups. –Independent variable—the variable being manipulated –Dependent variable—the response that is measured

Distribution of the data, showing the mean, for the control and the treatment.

P value allows us to have confidence in our results.

How do we know the results are not by chance alone?  P value statistics (p<.05 or p<.01) can help us evaluate whether differences between a treatment and control group can be attributed to the treatment rather than random chance.  The p-value tells us that 95% (p.01) of the time, the results are NOT by chance.

1.1.5 Deduce the significance of the difference between two sets of data using calculated values for the t and the appropriate tables We use a t-test to see if there is a significant (real) difference between to samples or two sets of data In other words, “Are the means far enough apart to call them truly different ?”

1.1.5 Deduce the significance of the difference between two sets of data using calculated values for the t and the appropriate tables (H o ) – There is no significant difference in the bill length between the two birds Excel can determine the P value directly. We don’t need the table for critical values Calculated value for P Much less than the value for p we use for biology = 0.05 If P<p, then we reject (H o ) The (H o ) is rejected – therefore there is a significant difference in bill length.

Correlation vs causation Trends between variables suggests causation, but does not prove it! Causation can only be demonstrated through the scientific method and good experimental design.

1.1.6 Explain that the existence of a correlation does not establish that there is a causal relationship between two variables

Correlation (r 2 ) statistics identify relationships (or the lack of relationships) between variables. Positive correlation As one variable increases, so does the other Negative Correlations As one variable increases, the other decreases No Correlation No relationship between the two variables.

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