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Statistics: Greenland (2016) Article
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Terms in this set (5)
What is a statistical model?
Statistical model: holds the assumptions about how data were collected and analyzed, and how the analysis results were selected for presentation for statistical inference
Mathematical model of data variability
Not only good presentation of data, but also hypothetical alternative data that might have been observed
If multiple outcome measures or multiple predictive factors are used, and if the decisions for data analysis have been chosen after data were collected
One assumption: particular effect has a specific size and has been targeted for statical analysis
This targeted assumption is called test hypothesis and the statistical methods used to evaluate it are called statistical hypothesis tests
Targeted effect size is a null value representing zero effect (e.g., that the study treatment makes no difference in average outcome)
In this case the hypothesis is called the null hypothesis (NHST)
We may test the hypothesis that the effect is no greater than a particular amount, in which the hypothesis is said to be a one-sided or dividing hypotheses
What is Probability in terms of a statistical model?
...
What does it mean for an isolated finding to be replicable/replicated?
What does it mean for an isolated finding to be replicable/replicated?
Two approaches: NHT vs. estimation
NHT: two statistical tests can replicate one another when they support same conclusion (non-rejection or rejection in a specific direction)
Estimation: two point or interval estimates are said to replicate one another when they meet some criterion of proximity (e.g., overlap of CIs)
Flaws of NHT (this is mostly repeat, but it could be helpful):
Null Hypothesis is "Quasi-Always" False, Testing It Is Uninformative
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Verified questions
STATISTICS
Researchers wanted to determine the association between number of times one chews food and food consumption. They identified 45 individuals who were 18 to 45 years of age. First, the researchers determined a baseline for number of chews before swallowing food. Next, each participant attended three sessions to eat pizza for lunch until comfortably full by chewing each portion of food 100%, 150%, and 200% of their baseline number of chews before swallowing. Food intake for each of the three chewing treatments was then measured. It was found that food consumption was reduced significantly, by 9.5% and 14.8%, respectively, for the 150% and 200% number of chews compared to the baseline. (a) What is the research objective of the study? (b) What is the response variable in this study? Is it quantitative or qualitative? (c) What is the explanatory variable in this study? ls it quantitative or qualitative? (d) Who are the experimental units? (e) How is control used in this study? (f) Each individual chewed 100%, 150%, and 200% of their baseline number of chews before swallowing. This is referred to as a repeated-measures study since the same participants were exposed to each treatment. The order in which chewing took place (100% versus 150% versus 200%) was determined randomly. Explain why this is important.
STATISTICS
The American Automobile Association (AAA) commissioned a study by researchers at the University of North Carolina on sources of distraction for drivers. The study tracked 70 drivers aged 18 to 80 for a week. Miniature cameras were placed in the drivers' cars, with their knowledge, and their driving behavior was randomly viewed for a week. The first three hours of each tape were discarded in the hope that drivers would act more naturally later in the week. The researchers considered a wide range of activities to be distracting, such as leaning over to reach for something, fiddling with radio controls, attending to babies, talking to passengers, applying makeup, and opening and reading their mail. The study found that 21 of the subjects used cell phones while their vehicles were moving. (a) Is there significant evidence that fewer than half of all drivers use cell phones while their vehicles are moving? Carry out appropriate inference, and report your results and conclusions. (b) Do you believe that this study is subject to bias? In what regard?
STATISTICS
Waterskiing and wakeboarding are two popular water-sports. Finding a model that best suits your intended needs, whether it is waterskiing, wakeboading, or general boating, can be a difficult task. WaterSki magazine did extensive testing for 88 boats and provided a wide variety of information to help consumers select the best boat. A portion of the data they reported for 20 boats with a length of between 20 and 22 feet follows (WaterSki, January/February 2006). Beam is the maximum width of the boat in inches, HP is the horsepower of the boat’s engine, and TopSpeed is the top speed in miles per hour (mph). $$ \begin{matrix} \text{Make and Model} & \text{Beam} & \text{HP} & \text{TopSpeed}\\ \hline \text{Calabria Cal Air Pro V-2} & \text{100} & \text{330} & \text{45.3}\\ \text{Correct Craft Air Nautique 210} & \text{91} & \text{330} & \text{47.3}\\ \text{Correct Craft Air Nautique SV-211} & \text{93} & \text{375} & \text{46.9}\\ \text{Correct Craft Ski Nautique 206 Limited} & \text{91} & \text{330} & \text{46.7}\\ \text{Gekko GTR 22} & \text{96} & \text{375} & \text{50.1}\\ \text{Gekko GTS 20} & \text{83} & \text{375} & \text{52.2}\\ \text{Malibu Response LXi} & \text{93.5} & \text{340} & \text{47.2}\\ \text{Malibu Sunsettter LXi} & \text{98} & \text{400} & \text{46}\\ \text{Malibu Sunsetter 21 XTi} & \text{98} & \text{340} & \text{44}\\ \text{Malibu Sunscape 21 LSV} & \text{98} & \text{400} & \text{47.5}\\ \text{Malibu Wakesetter 21 XTi} & \text{98} & \text{340} & \text{44.9}\\ \text{Malibu Wakesetter VLX} & \text{98} & \text{400} & \text{47.3}\\ \text{Malibu vRide } & \text{93.5} & \text{340} & \text{44.5}\\ \text{Malibu Ride XTi} & \text{93.5} & \text{320} & \text{44.5}\\ \text{Mastercraft ProStar 209} & \text{96} & \text{350} & \text{42.5}\\ \text{Mastercraft X-1} & \text{90} & \text{310} & \text{45.8}\\ \text{Mastercraft X-2} & \text{94} & \text{310} & \text{42.8}\\ \text{Mastercraft X-9} & \text{96} & \text{350} & \text{43.2}\\ \text{MB Sports 190 Plus} & \text{92} & \text{330} & \text{45.3}\\ \text{Svfara SVONE} & \text{91} & \text{330} & \text{47.7}\\ \end{matrix} $$ a. Using these data, develop an estimated regression equation relating the top speed with the boat’s beam and horsepower rating. b. The Svfara SV609 has a beam of 85 inches and an engine with a 330 horsepower rating. Use the estimated regression equation developed in part (a) to estimate the top speed for the Svfara SV609.
PROBABILITY
The weights of babies born at Prince Louis Maternity Hospital last year averaged 3.0 kg with a standard deviation of 200 grams. If there were 545 babies born at this hospital last year, estimate the number that weighed: a. less than 3.2 kg b. between 2.8 kg and 3.4 kg.