2022 Introduction to Statistics in Research Mitchell 2nd ed

I N T R O T O R E S E A R C H : D A T A V I S U A L I Z A T I O N & C O M M O N S T A T T E S T S

MOTHER SMOKES

The z score of a 9-pound baby in the Mother Smokes group is 2.36 calculated as follows:

=(9-6.5)/1.06 = 2.36

This means that a 9 pound baby in the Mother smokes is 2.36 standard deviations above the mean.

MOTHER NEVER SMOKED

The z score of a 9-pound baby in the Mother never smoked group is 1.43 calculated as follows:

=(9-7.2)/1.26 = 1.43

This means that a 9-pound baby in the Mother never smoked is 1.43 standard deviations above the mean.

Q4: Could you conclude from these data that smoking causes lower birth weights?

This is data from an observational study, NOT an EXPERIMENT, so we can't establish causation. Even with more data, you still would not prove that smoking caused lower birth weights.

Advanced Analysis – just a peak One of the neatest scenarios in statistics was presented by Statistics by Jim

Jim is a Star Trek fan (me too!) and he surmised that crewman on Star Trek who wore red shirts have the unfortunate reputation of being the first to die. The colors of the uniforms are blue, red, and yellow. Shirt color is a categorical variable, and the chi-squared test is a perfect test to use to see if this reputation has any truth. Statistics by Jim explains some of this as well, so I'm summarizing...

So first, the null hypothesis : There is no relationship between the categorical variables. Knowing the value of one variable will not help you predict the value of another variable. (Quiz)

The alternative hypothesis : There is a relationship between the categorical variables.

Essentially, the alternative hypothesis, the independent variable did affect the dependent variable, and the results are significant in terms of the investigation.

For a chi-square test, a p -value is used to help us determine if they are significantly different. A p -value (or probability value) is a number describing the likeliness of the data that would have occurred by random chance (i.e. that the null hypothesis is true). The smaller the p -value, the stronger the evidence that you should REJECT the null hypothesis.

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