2Quantitative DataQuantitative – measured using a naturally occurring numerical scaleExamplesChemical concentrationTemperatureLengthWeight…etc.4/5/2017
3Qualitative DataInformation that relates to characteristics or description (observable qualities)Information is often grouped by descriptive categoryExamplesSpecies of plantType of insectShades of colorRank of flavor in taste testingRemember: qualitative data can be “scored” and evaluated numerically4/5/2017
4Sampling DataDon’t have enough time or resources to measure every individual in a population.Choose and measure a representative sample from a population.Need to have a good SAMPLE SIZE in order to “believe” your data. (statistically significant)4/5/2017
6Displaying the dataError bars can be added to graphs to show the range of data.This shows the highest and lowest values of the data.
7Mean Another word for the average Calculated by summing the values and then dividing by the number of values obtained.Symbol: x
8Statistical analysis of a sample Mean: is the average of data pointsRange: range is the measure of the spread of dataStandard Deviation: is a measure of how the individual observation of data set are dispersed or spread out around the mean4/5/2017
9What does the standard deviation measure The standard deviation measures how spread out your values are.If the standard deviation is small, the values are close together.If the standard deviation is large, the values are spread out.It is measured in the same units as the original data.
10Standard deviation Measures the spread of data around the mean. Formula: s = √(x - x )2BUT you do not need to remember it.You must be able to calculate it on your calculators (or spreadsheet in the lab)
11Standard DeviationThe standard deviation tells us how tightly the data points are clustered togetherWhen standard deviation is small—data points are clustered very closeWhen standard deviation is large—data points are spread out4/5/2017
12Standard DeviationWe will use standard deviation to summarize the spread of values around the mean and to compare the means and spread of data between two or more sampleIn a normal distribution, about 68% of all values lie within ±1 standard deviation of the meanThis rises to about 95% for ±2 standard deviation from the mean4/5/2017
16Why is it useful? Calculate the mean of 100, 200, 300, 400, 500. Now let's imagine you had the values 298, 299, 300, 301, 302. Calculate the mean of these numbers.Although the two means are the same, the original data are very different.
17The standard deviation will reflect this difference. The standard deviation of 100, 200, 300, 400, 500 is 141.4The standard deviation of 298, 299, 300, 301, 302 isSo the standard deviation of the first set of values is 100 times as big - these data are 100 times more spread out.
19Error BarsTo graphically display data, you will use the CI to generate error bars.Error bars represent the spread around the mean.4/5/2017
20Comparing Means -What can you conclude when error bars do overlap? When error bars overlap, you can be sure the difference between the two means is not statistically significant. (Due to chance variations)What can you conclude when error bars do not overlap? When error bars do not overlap, you cannot be sure that the difference between two means is statistically significant. T-test is commonly used to compare these groups.4/5/2017
24Why do I need both the mean and standard deviation? Although the standard deviation tells you about how spread out the values are, it doesn't actually tell you about the size of them.For example, the data 1,2,3,4,5 have the same standard deviation as the data 298,299, 300,301,302
25Displaying the dataError bars can be added to graphs to show the standard deviation.This shows the spread around the mean.
26Confidence Interval (CI) 95% certain the mean will be found within the interval4/5/2017
27T-testA common form of data analysis is to compare two sets of data to see if they are the same or differentNull hypothesis: there is NO significant difference between
28T-test Calculate a value for “t” Compare value to a critical value (0.05 column)If “t” is equal to or higher than the critical value we can reject the null hypothesis.
29CorrelationCorrelation is a measure of the association between two factors. The strength of the association between two factors can be measured.An association in which all the values closely follow the trend is described as being a strong correlation.An association in which there is much variation, with many values being far from the trend, is described as being a weak correlation.A value can be given to the strength of the correlation, r.r = +1 a complete positive correlationr = 0 no correlationr = -1 a complete negative correlation4/5/2017