Introduction to statistics August 19, 2014 Pick up your science journal at the front. Hold onto your IA fruit ripening comments.

Essential Questions What is scientific inquiry? How do we define results to be significant?

The Vitruvian Man Ideal human proportions described by Roman architect Vitruvius the length of the outspread arms is equal to the height of a man from below the chin to the top of the head is one-eighth of the height of a man from above the chest to the hairline is one-seventh of the height of a man. the maximum width of the shoulders is a quarter of the height of a man. the distance from the elbow to the armpit is one-eighth of the height of a man. the length of the hand is one-tenth of the height of a man. the foot is one-seventh of the height of a man. from below the foot to below the knee is a quarter of the height of a man. from below the knee to the root of the penis is a quarter of the height of a man. The drawing is based on the correlations of ideal human proportions with geometry described by the ancient Roman architect Vitruvius in Book III of his treatise De Architectura. Vitruvius described the human figure as being the principal source of proportion among the Classical orders of architecture. Vitruvius determined that the ideal body should be eight heads high. Leonardo's drawing is traditionally named in honor of the architect.

Pick up your science journal at the front. Statistics August 21, 2014 Pick up your science journal at the front.

CONTINUOUS? DISCRETE?

Standard deviation Used to summarize the spread of values around the mean 68% of the values fall within one standard deviation of the mean.

Standard deviation A small standard deviation indicates that the data is clustered closely around the mean value A large standard deviation indicates a wider spread around the mean

Error bars Error bars are graphical representation of the variability of data (standard deviation)

T-test Used to determine whether there is a significant difference between means of two populations Examples: Compare the size of beak for two kinds of finches Compare the heart rate before/after drinking coffee When is it ‘significant’? There is a significant difference when the difference is caused by a factor other than chance To use a t-test, samples must be greater than 10

When can we say that something is significant? P = probability that the difference is due to chance If P < 0.05 (or 5%) The probability that the two groups is different is due to less than 5% chance 95% due to ‘something other than chance’ = 95% confidence level There is a significant difference between two groups If P > 0.05 The probability that the two groups is different is due to greater than than 5% chance Less than 95% due to ‘something other than chance’ = 95% confidence level There is no significant difference between two groups

How do we know when results support a conclusion? Statistics t-test How do we know when results support a conclusion? TODAY: In your blog: What is the significance of the t-test? What is the p-value? This week’s feedback distributer: Silvana ANNOUCEMENT: Quiz Lab due date

T-test Used to determine whether there is a significant difference between means of two populations Sample size of at least 10 required

Instructions (1) Command terms quiz Finish first t-test sheet and show me. Go on to the second t-test packet. Begin to work on your lab (ONLY DCP & CE). For your DCP, include: all calculations (means, SD, t-test) and graphs you created. Follow the IA guidelines VERY carefully on formatting of the data.

How do we know when results support a conclusion? Statistics t-test How do we know when results support a conclusion? TODAY: In your blog: What is a correlation? How is it different from causation? This week’s feedback distributer: Silvana ANNOUCEMENT:

Correlation suggests relationships between two sets of data Some causal relationships Temperature vs enzyme activity Concentration vs rate of diffusion CO2 concentration vs rate of photosynthesis Need to have carefully controlled variables

Examples of correlation

Correlation equals causation?

Instructions Finish t-test packet. SHOW me when you are done! Begin to work on your lab (ONLY DCP & CE). For your DCP, include: all calculations (means, SD, t-test) and graphs you created. Follow the IA guidelines VERY carefully on formatting of the data. Make a star by the sections you don’t understand in the rubric/IA guide and ask me questions.