1. Statistical Analysis I have all this data. Now what does it mean?

2. Can you say that a bean plant will grow taller with 50 mL of water instead of 25 mL?

3. Is your data Quantitative or Qualitative? Continuous quantitative – measurement scale divisible into partial units Ex-Distance in kilometers Discrete quantitative - measurement scale with whole integers only Ex- number of wolves born in given year Quantitative data can be subdivided into: Ratio - with equal divisible intervals & absolute zero Interval - does not have absolute zero Qualitative Nominal - objects are named or can’t be ranked Example- Gender (male/female) Qualitative Ordinal - objects are placed into categories that can be ranked Example- activity of an animal on a scale of 1 to 5 Decide which type of data you have__________________

4. Describing data Central tendency (How different 2 sets of Data is) Mode - value that occurs most often Mode - value that occurs most often Median - middle value when ranked highest to lowest Median - middle value when ranked highest to lowest Mean - mathematical average Mean - mathematical average Variation (How spread out the data is) For quantitative data – Range, For quantitative data – Range, Standard Deviation σ, Variance σ 2 http://www.mathsisfun.com/data/standard-deviation.html http://www.mathsisfun.com/data/standard-deviation.html For qualitative data - Frequency distribution For qualitative data - Frequency distribution chi square by paul anderson chi square by paul anderson Frequency Distribution Frequency Distribution

5. Statistics Software … is not going to do your job for you. It is: not going to tell you what test to select not going to tell you if the test you selected is the right one not going to tell you how to interpret the test results.

6. Making decisions about descriptive statistics & Graphs Decide which type of data you have, parameters you will need to calculate and on your Excel chart, enter the formula for each of the parameters. Quantitative DataQualitative ParametersRatio dataInterval dataNominal dataOrdinal data Type of datadata collected using a scale with equal intervals and with an absolute zero (distance, velocity) using a scale with equal intervals but no absolute zero (temp 0 C, pH) objects are placed into categories that cannot be ranked (male/female or brown, black, red hair) objects are placed into categories that can be ranked (Moh’s hardness scale or color ranked 1- 10) Central tendencyMean Mode Median VariationRange Standard deviation Variance Range Standard deviation Variance Frequency Distribution Degrees of freedom Total # of samples - 2 (ex. 15+15-2 = 28) Total # of samples - 2 (ex. 15+15-2 = 28) (#rows –1) x (#columns-1) Level of significance 0.025 0.05

7. Inferential Statistics Is the data statistically significant? NOT due to random chance or error or uncontrolled variable Statistical Tests The t-test (or Analysis of Variance): two or more groups to compare measurements of each group. The Chi-square test: counts that can be placed into yes or no categories, or categories such as quadrants. The Pearson R Correlation: to test how the values of one event or object relates to the values of another event or object

8. How to select statistical test? Is Dependent Variable (DV) continuous, ordinal, or nominal? Dependent Variable (DV) continuous Continuous IV T-test or ANOVA Scatter plot Nominal IV T-test or ANOVA Bar graph of means Ordinal IV T-test Bar graph of means

9. Dependent Variable (DV) Ordinal Continuous IV Chi-square Scatter plot Or Histogram Nominal IV Mann- Whitney’s test Bar of means Ordinal IV Spearman’s test Scatter plot

10. Dependent Variable (DV) Nominal Continuous IV T-test or F-test Bar graph of means Nominal IV Paired-Mcnemar’s Unpaired-Chi- square Bar graph of proportions Ordinal IV Spearman’s test Scatter plot

11. Null Hypothesis (μ) …..states that there is NO difference between the mean of your control group and the mean of your experimental group. Therefore any observed difference between the two sample means occurred by chance and is not statistically significant. If you can reject your null hypothesis then there is a significant difference between your control and experimental groups. Hence accept the alternative (original hypothesis). If you can reject your null hypothesis then there is a significant difference between your control and experimental groups. Hence accept the alternative (original hypothesis). Write your null hypothesis _____________________________

12. Probability - Chance Could the difference between the groups due to random chance /error? Probability of error or p-value < 0.05 means that the error in the research is 5/100 or below 0.05 (95% results have no error) P<0.05 Less than 5% chance is considered to be OK. Reject Null hypothesis Accept your alternative (original) hypothesis P>0.05 Greater than 5% then the data is not significant. Must accept Null hypothesis

13. Level of significance (  ) and Degree of freedom (df) Level of significance (  ) - It communicates probability of error in rejecting Null hypothesis p-value < 0.05 p-value < 0.05 means that the probability of error in the research is 5/100 (95% results with no error) Degree of freedom (df) - It is number of independent observations in a sample. t-test df = (n1-1) + (n2-1) Chi-square df = (#rows – 1) (#columns – 1) Pearson R correlation df = (n-2) subtract 2 from the number of comparisons made. T test Chi square tables.doc

14. Accept or Reject the null hypothesis Find the table value for t-test and Chi-square test (using calculated degrees of freedom and Level of Significance of 0.05 = 95%) Compare calculated value to table value. Calculated value 0.05 Null hypothesis is accepted Calculated value > or = table value means P or = table value means P<0.05 Null hypothesis is rejected. s/w does it for you, and will show you p-value If P<0.05 then reject Null & accept alternative hypothesis