Bar & Pie Chart Appropriately | Analyze Contingency Tables Three Ways ‘Making a Picture’ Helps in Data Analysis A display of data will help reveal things that would be obfuscated in a table of numbers, and it will help you plan your analysis and think clearly about the relationships/patterns in your data. A display will do much of the work of analyzing data. It can show important features/patterns. A picture will also reveal unexpected patterns or extraordinary (possibly wrong) data values. A we

Displaying Data Distributions Histograms Like a bar chart, a histogram plots the bin counts as the heights of bars. A bin is one of the groups of values on the horizontal axis of the histogram. Unlike a bar chart, which puts gaps between bars to separate the categories, no gaps appear between the bars of a histogram unless there are actual gaps in the data. Gaps can be important, so watch out for them. How Do Histograms Work? First, you would need to decide how wide to make the bins. The width

When to Use Scatterplots? Scatterplots are the best way to start observing the relationship between 2 quantitative variables. By looking at a scatterplot you can see patterns, trends, relationships, and outliers. What to Look for in Scatterplots? Direction An upward sloping line is said to be positive. A downward sloping line is said to be negative. Form Is the association linear? Or does it go sharply up & sharply down again? Straight-line patterns are both the most common & the most useful f

Random Phenomena & Empirical Probability What is Random Phenomena? With random phenomena, we can’t predict the individual outcomes, but we can hope to understand characteristics of their long-run behaviours. We don’t know whether the next caller will qualify for a reward, but as calls come into a call centre, the company will find that the percentage of qualified callers will settle into a pattern, like that shown in this graph. Key Terms & Definitions Trial - An attempt Outcome (Event) - Each

Expected Value of a Random Variable Defining Key Terms Random Variable Terms Random Variable: Variables whose values are based on the outcome of a random event. Capital letters (X) denote a random variable. Lowercase letters (x) denote a particular value that it can have. Discrete Random Variable: If you can list all the outcomes, it’s a discrete random variable. Continuous Random Variable: A random variable that can take on any value between 2 values. Probability Terms Probability Distribution:

Modelling Sample Proportions What is True Proportion? Say we take many random samples of 1000 people and find the proportion of each sample being male. Let’s collect all those proportions into a histogram. Where would the centre of the histogram be? We don’t know. But it’s reasonable to think that it’ll be very close to the true proportion. We’ll likely never know the value of the true proportion, but it’s important so we give it a label (p). Using Simulations A computer can pretend to draw rand

A Confidence Interval Confidence Intervals; Margin of Error; Critical Values; Assumptions & Conditions; Sample What do we know about the Sampling Distribution model? We know that it’s centred at the true proportion, p. But we don’t know p. Let’s say we know a p̂. What we do know is that the sampling distribution model of p̂ is centred at p, and we know that the standard deviation of the sampling distribution is . We also know, from the Central Limit Theorem, that the shape of the sampling dist

Hypotheses What is a Hypothesis? A supposition; a proposition or principle which is supposed or taken for granted, in order to draw a conclusion or inference for proof of the point in question; something not proved but assumed for the purpose of argument. Null Hypothesis Suppose a video provider knows that 67% of its current customers are satisfied with the video recommendations it provides. It then launches a trial of a new recommendation algorithm for some customers and surveys 1000 of those

The Sampling Distribution for the Mean Confidence Intervals for Means Recall, the confidence interval for proportions is such: Where is equal to Our confidence intervals for means will be similar: Where is equal to a critical value times The Central Limit Theorem on Means When a random sample is drawn from any popul

t-Test on the Difference of 2 Means; Confidence Interval for Difference of 2 Means; Hypothesis Tests for Difference of Means Comparing Two Means Suppose a company wants to know if credit card promotions (ex: points) increases spending. To test, they measure two samples of users; (1) users who received the promotion, and (2) users who did not. We can see, on the boxplot, that the users who were offered the promotion have a higher mean. But more statistical analysis is required before we can say