Chapter 1-2 Review MDM 4U Mr. Lieff

Ch1 Learning Goals Classify data as Quantitative (and continous or discrete) or Qualitatitive Identify the population, sample and main variables in a study Tell a story from a graph (draw conclusions) Use the equation from a trendline to calculate values Differentiate between the Median-Median and Least-Squares Lines Describe a correlation (positive or negative, strong or weak) Connect a scatter plot to an r or r 2 value Identify misleading features of a graph

1.1 Displaying Data Visually Types of data Quantitative Discrete – only whole numbers are possible Continuous – decimals/fractions are possible Qualitative / Categorical – non-numeric Population – the group being studied Census – data is collected from every member Sample – data is collected from a subset of the pop’n

1.1 Displaying Data Visually Frequency Table, Stem and Leaf Plot Measures of Central Tendency (mean/median/mode) Read information from the following graphs; know when to use them One variable Bar Graph (qualitative or discrete data) Histogram (data in intervals or continuous data) Broken Line Graph (one variable over time) Pie Graph (comparing quantities to a whole) Two variable Scatter Plot (compare two numeric variables) Stacked Bar Graph (individual frequencies of two variables) Double-Bar Graph (total frequencies of two variables)

1.2 One Variable Data When can we draw conclusions? Must see a trend Must have a representative sample Correlation - a change in one variable is observed with a change in another Can be seen on a scatter plot Causal Relationship – a change in one variable causes a change in another Requires an in-depth study

1.3 Visualizing Trends Variables Independent (x-axis) Dependent (y-axis) Syntax for graphing: dependent vs. independent e.g., weight vs. height Scatter Plots and Correlations Trends – positive/negative (or none); weak/strong Lines of Best Fit Median-Median – based on 3 median points Least Squares Line – based on residuals (every point)

1.4 Trends in Technology Regression (can be linear or non-linear) Correlation Coefficient r (-1 to 1) Describes strength and direction of correlation Coefficient of Determination r 2 (0 to 1) Gives the % of the change in y that is due to x Residuals Vertical distances between point and line of best fit The Least Squares line minimizes the sum of the squares of the residuals

1.5 – Misuse of Data 3D graphs are distorted Changing the scale Distorts differences / changes Small sample May allow you to draw invalid conclusions

Review pp # 1, 3-10 * you will not have to create a scatter plot on the test * see next 2 slides for graphs for #3 & 6

p. 72 #3

p. 72 #6

Ch2 Learning Goals Differentiate between a cross-sectional and longitudinal study Clinical Studies – identify Treatment, Placebo, Treatment and Control groups Describe how to take a random sample Simple, Systematic, Stratified, Cluster, Multi- Stage Identify types of bias: Sampling, Non- Response, Household, Response

2.2 – In Search of Good Data What are the variables in a study? The information that is collected What types of variables exist? Quantitative Continuous – decimals are possible Discrete – only whole numbers Qualitative - description Types of Studies Cross-Sectional – data is collected once Longitudinal – the same data is collected multiple times in regular intervals

2.3 Collecting Samples Why do we sample? Census is expensive and time consuming Valid inferences can be made from a representative sample Convenience sampling – not representative Clinical Studies Treatment – the active drug Treatment Group – gets the drug Control Group – gets a treatment with no value Placebo – a placeholder for the drug Double Blind Test – neither the participants nor the researchers know who gets the treatment

2.4 Random Sampling Methods Simple – names in a hat; generate random numbers Systematic sampling interval n = (population size) ÷ (sample size) Generate a random starting point between 1 and n Start there and sample every n th member Stratified – grouped population; take a proportional simple random sample of each group Cluster – grouped population; randomly select groups and sample entire group Multistage – grouped population; randomly select groups and take a simple random sample of each group

2.4 Destructive Sampling Destructive Sampling – tested element cannot be returned to the population batteries, lightbulbs, cars, standardized testing Ex: destructive simple random sample: pick 10 batteries out of a bin of 100 and test Ex: destructive systematic random sample: test every 10 th battery (10% sample)

2.5 Types of Bias Sampling Bias – poorly chosen sample Non-Response Bias – selected respondents do not provide data Household Bias – groups are not represented proportionally Response Bias – problems with the survey or surveyor

Chapter 2 Review pp #1abd, 2, 4–8 #7: Canada’s Population million (2013)