Chapter 4 Lecture Notes Inferential Statistics and Normal Curve Table PDF

Preview

Summary

Lecture notes from Professor Brent Costleigh's class....

Description

Some Key Ingredients for Inferential Statistics ● Inferential statistics ○ Allows us to draw conclusions about theoretical principles that go beyond the group of participants in a particular study ○ Applying experimental results to larger group (population) ● The normal curve ○ Normal distribution ■ Represents histogram or frequency distribution that is unimodal, symmetrical, and bell shaped ■ Mathematical distribution ■ Researchers compare the distributions of their variables to see if they approximately follow the normal curve ○ Why it is commonly found in nature ■ A person’s ratings on a variable or performance on a task is influenced by a number of random factors at each point in time ■ These factors can make a person rate things like stress levels or mood as higher or lower than they actually are, or can make a person perform better or worse than they usually would ■ Most of these positive and negative influences on performance or ratings cancel each other out ■ Most scores will fall toward the middle, with few very low scores and few very high scores ● This results in an approximately normal distribution (unimodal, symmetrical, and bell-shaped) ○ 2%-14%-34%-14%-2% → The normal curve and the percentage of scores between the mean and standard deviations from the mean (50-34-14 rule) ■ Roughly 4% of scores are more than 2 standard deviations from the mean ● The normal curve table and z scores ○ The normal curve table (page 435) shows the percentages of scores associated with the normal curve ■ The first column of this table lists the z score ■ The second column is labeled “% mean to z” and gives the percentage of scores between the mean and that z score ■ The third column is labeled “% in tail” ■ To find the “body %” just find “% in tail” and subtract from 100, or find “% mean to z” and add 50 ● Using the normal curve table to figure a percentage of scores above or below a raw score ○ If you are beginning with a raw score, first change it to a z score ■ Z = (x-m) / SD ○ Draw the normal curve, decide where the z score falls on it, and shade in the area for which you are finding the percentage

○

●

●

●

●

●

Make a rough estimate of the shaded area’s percentage based on the 50-34-14 percentages ○ Find the exact percentages using the normal curve table ■ Look up z score in z column ■ Find percentage in the % mean to z column or the % in tail column ■ Check that your exact percentage is within the range of your rough estimate Using the normal curve table to figure z scores and raw scores ○ Draw a picture of the normal curve and shade the approximate area of percentage ○ Make a rough estimate of the z score where the shaded area stops ○ Find the exact z score using the normal curve table ○ Check that your z score is within the range of your rough estimate ○ Convert z score to raw score ■ X = (z)(sd) + m Sample and population ○ Population - an entire set of things of interest ■ The entire piggy bank of pennies ■ The entire population of individuals in the US ○ Sample - the part of the population about which you actually have information ■ A handful of pennies ■ 100 men and women who answered an online questionnaire about health care usage Why samples instead of populations are studied ○ It is usually more practical to obtain information from a sample than from the entire population ○ The goal of research is to make generalizations or predictions about populations or events in general Methods of sampling ○ Random selection - method of choosing a sample in which each individual in the population has an equal chance of being selected ■ Using a random number table ○ Haphazard selection - method of selecting a sample of individuals to study by taking whoever is available or happens to be first on a list ■ This method of selection can result in a sample that is not representative of the population Statistical terminology for sample and populations ○ Population parameters: mean, variance, and standard deviation of a population ■ Usually unknown and can be estimated from information obtained from a sample of the population ○ Sample statistics: mean, variance, and standard deviation you figure for the sample ■ Calculated from known information

●

●

●

●

●

●

Probability: the expected relative frequency of a particular outcome ○ Outcome - term used for discussing probability for the result of an experiment ○ Expected relative frequency - number of successful outcomes divided by the number of total outcomes you would expect to get if you repeated an experiment a large number of times ■ This is the long-run relative-frequency interpretation of probability ● Understanding of probability as the proportion of a particular outcome that you would get if the experiment were repeated many times Steps for figuring probability ○ Determine the number of possible successful outcomes ○ Determine the number of all possible outcomes ○ Divide Range of probabilities ○ Probability cannot be less than 0 or greater than 1 (0%-100%) ■ Something with a probability of 0 has no chance of happening ■ Something with a probability of 1 has 100% chance of happening P stands for probability ○ Probability is usually written as a decimal, but can also be written as a fraction or percentage ○ P < 0.05 ■ The probability is less than 0.05 ■ Variability decreases the likelihood to find an effect (found in small samples) Probability, z scores, and the normal distribution ○ The normal distribution can also be thought of as a probability distribution ■ The percentage of scores between 2 z scores is the same as the probability of selecting a score between those z scores Normal curves, samples, and populations, and probability in research articles ○ Normal curve is sometimes mentioned in the context of describing a pattern of scores on a particular variable ○ Probability is discussed in the context of reporting statistical significance of study results ○ Sample selection is usually mentioned in the methods section of a research article...