Statistics notes 8/10/14 Bell Ringer: How could you organize an experiment so that the results showed something completely different from the truth?

Descriptive vs Inferential Statistics Descriptive statistics consists of the collection, organization, summarization, and presentation of data. Inferential statistics consists of generalizing from samples to populations, performing estimations and hypothesis tests, determining relationships among variables, and making predictions

Sampling Styles Random – Selected by using chance methods or random numbers Systematic – Selecting every k th subject in a population Stratified – Population is separated into groups and then randomly chosen within the groups Cluster – Separate the population into representative groups and use all of the subjects inside the selected clusters

Convenience Sampling Convenience Sampling is done by choosing the subjects simply by what is simplest for the researcher. This can lead to very inaccurate results because of high levels of bias in the sample.

Observation vs Experiment Observational studies are merely observing what is happening or what has happened and trying to draw conclusions from the data Experimental studies are manipulating one of the variables to try to determine how the manipulation influences the others.

Treatment vs Control Experiments have at least one treatment group and at least one control group Treatment group is the one that receives the change in the independent variable Control group gets the normal experience without a change in the independent variable.

Types of variables Independent variable – The variable being manipulated by the researcher – Also called the explanatory variable Dependent variable – The variable being measured for change as a result of the independent variable change – Also called the outcome variable Confounding variables – Variables that can influence the dependent variable but cannot be separated from the independent.

Misuses of Stats “There are three types of lies---lies, lies and statistics” “Figures don’t lie, but liars figure.” “83.6% of all statistics are made up on the spot.”

Suspect samples Very small samples Biased samples – Volunteer Samples – Convenience samples – Opinion Polls

Ambiguous Averages 4 different terms can be referred to as averages – Mean – Median – Mode – Midrange These can differ by a good bit in samples and if the research does not tell which it used, it can be purposely misleading

Changing the Subject Changing the way in which you refer to the data can greatly influence how it is seen. Example – “In my term, the deficit raised only 1%” may be used by a politician – “In my opponent's term, the deficit was raised by a whopping $8,000,000!” may be used by his opponent – While both are correct, the elicit two different reactions.

Detached Statistics Making a claim with no comparison Example – My new headache medicine works 3 times faster! – 3 times faster than what?

Implied Connections Using language that implies that results will come but is not legally saying that they will. Example – Studies suggest that using our exercise machine will reduce your weight – Using the word suggest gets them around havng to back up the claim Watch for words like may, in some people, and might help, as well as suggest.

Misleading graphs Graphs are used almost always to get the main portion of the data across, but if they are used in a misleading way, they can show a much different picture.

Correct Graph

Faulty survey questions Survey questions are carefully crafted to either remove bias or to influence the results in the way the writer wants. Examples – “Do you support building a new Cascade High School?” – “Do you support raising taxes so that we can build another new high school out in Wartrace?” – These are the same thing but one is worded to get the negative resonse.

Correlation vs causation