STATISTICS Topic 1 IB Biology Miss Werba

TYPES OF STATISTICAL DATA 1.1 TYPES OF STATISTICAL DATA DATA TYPE EXAMPLE CENTRAL TENDENCY NOMINAL Named categories Mode ORDINAL Ranked or relative data Median INTERVAL On a scale (normally distributed) Mean J WERBA – IB BIOLOGY 2

CALCULATING THE ARITHMETIC MEAN 1.1 CALCULATING THE ARITHMETIC MEAN Find the average of the individual conditions Measure of central tendency The formula for the arithmetic mean is: where, = arithmetic mean = sum of all measurements = total no. of measurements J WERBA – IB BIOLOGY 3

1.1 ERROR BARS Variability: differences in various traits that exist between members of a population All data has some degree of associated error. This error is presented by error bars on a graph. Error bars also allow us to record the degree of variability in the readings. Error bars typically show either: range standard deviation 95% confidence intervals (CI) J WERBA – IB BIOLOGY 4

CALCULATING THE STANDARD DEVIATION 1.1 CALCULATING THE STANDARD DEVIATION The standard deviation of the mean tells us how spread out the readings are. A small S.D. indicates a small range of data A large S.D. indicates a large range of data J WERBA – IB BIOLOGY 5

SPREAD OF DATA Large standard deviation Small standard deviation 1.3 1.4 SPREAD OF DATA Large standard deviation Small standard deviation J WERBA – IB BIOLOGY 6

SPREAD OF DATA The standard deviation is used to show data spread 1.3 1.4 SPREAD OF DATA The standard deviation is used to show data spread 68% of data falls within one S.D. of the mean 95% of data falls within two S.D. of the mean 99% of data falls within three S.D. of the mean J WERBA – IB BIOLOGY 7

SPREAD OF DATA Standard deviation is useful for : 1.3 1.4 SPREAD OF DATA Standard deviation is useful for : comparing means comparing the spread of data between two or more samples When considering multiple samples, the closer the means and S.Ds, the more likely that the samples have been drawn from similar (or the same) populations. If the S.D. is greater than the difference between two means, then the difference is not statistically significant Remember: small samples are unreliable!!!!!!!!!!!!!! J WERBA – IB BIOLOGY 8

STUDENT t-TEST Used to compare 2 populations 1.5 STUDENT t-TEST Used to compare 2 populations The size of sample determines the reliability of the results. The t-test shows the significance of the difference between two sets of data: Large t-values indicate a significant difference between the two sets of data. Small t-values indicate little to no difference between the populations. J WERBA – IB BIOLOGY 9

1.5 STUDENT t-TEST Need to either prove or disprove your experimental hypothesis : H0 = null hypothesis H1 = experimental hypothesis  that the IV affects the DV J WERBA – IB BIOLOGY 10

STUDENT t-TEST Choose a one-tailed or two-tailed t-test: 1.5 STUDENT t-TEST Choose a one-tailed or two-tailed t-test: 1-tailed = there is an effect (one of +ve or –ve) 2-tailed = there is an effect (either +ve or –ve) Choose a paired or unpaired: paired = same organisms measured in difft conditions unpaired = difft organisms measured in difft conditions J WERBA – IB BIOLOGY 11

STUDENT t-TEST Select your degrees of freedom: Select your p-value: 1.5 STUDENT t-TEST Select your degrees of freedom: Degrees of freedom = sample size (n) - 1 This occurs for each group - ie. two groups = (n1 +n2) - 2 Select your p-value: Generally use p = 0.05 If H1 is supported, it will indicate that you are 99.95% confident that the IV had a significant effect on the DV J WERBA – IB BIOLOGY 12

STUDENT t-TEST Calculate the t-value: 1.5 STUDENT t-TEST Calculate the t-value: Use formula, calculator or Excel Compare t-value to t-test data table: If t-value exceed p=0.05 value, then data is significant Reject the null hypothesis and accept the experimental hypothesis J WERBA – IB BIOLOGY 13

CORRELATION vs CAUSATION 1.6 CORRELATION vs CAUSATION Correlation means that there is a relationship between two (or more) things. This DOES NOT MEAN that one has caused the other to occur. There might be a common event that causes bother events to occur. t-tests show a correlation between the two sets of data but does not prove a causal relationship…. J WERBA – IB BIOLOGY 14

CORRELATION vs CAUSATION 1.6 CORRELATION vs CAUSATION Correlation describes the strength and direction of a linear relationship between two variables Use the Pearson correlation coefficient (r): +1  strong, positive correlation 0  no correlation –1  strong, negative correlation Used if data is continuous and normally distributed A line of best fit is obtained from a scatter plot of the data points and the gradient is obtained. J WERBA – IB BIOLOGY 15

CORRELATION vs CAUSATION 1.6 CORRELATION vs CAUSATION J WERBA – IB BIOLOGY 16