PSYCH 311 1st Edition Exam 2 Study Guide Lectures 6 13 Lecture 6 September 10 Samples and Populations Samples are either biased or unbiased with the mean always being unbiased because it always underestimates population variance while the variance or standard deviation is biased because it always underestimates population variance Use degrees of freedom to correct the bias and calculate variance and standard deviation Df 1 X N population X M n 1 sample Lecture 7 September 17 How do you determine Z Scores Standardizing a distribution is making two different distributions the same in terms of their mean and standard deviation Use the Z score formula of Z X The Z score can specify a location and tell you where the score falls relative to the mean and the number value tells you how far the score falls from the mean in units of standard deviation What is a standardized distribution A standardized distribution is a distribution composed of raw scores transformed into z scores therefore a Z Distribution is a standardized distribution In a Z Distribution the mean will always be zero the standard deviation will always be 1 0 and the shape will always be identical to the shape of the raw distribution Standardizing distributions allow you to make comparisons between two unalike sets of data Percentile Scores Each section under a distribution represents a percent of the entire distribution In a standard score Z scores are expressed relative to the sample although the interpretation of it is dependent on sample distribution Extreme scores are scores that have a Z distribution beyond two standard deviations from the mean in either direction Lecture 9 September 24 What is inferential statistics Inferential statistics is a statistical technique that allows us to study samples and make generalizations about the population they are drawn from It states that whatever is true about the sample is true about the population The problem is the sampling error the discrepancy between sample and population that is always present But by understanding probabilities we can have a better understanding of how to interpret the affect of the sampling error on the process What are Probabilities and Proportions Probabilities are there are the fraction or proportion of the total number of possible outcomes for any particular outcome it is the likelihood that something will happen Proportions on the other hand are the physical area or specific section of the whole Probabilities are expressed in terms of fractions while proportions are expressed in decimal form with a range of 0 00 1 00 Yet proportions and probabilities can be used interchangeably if expressed in terms of percentages What is random sampling Random sampling is unbiased sampling it is when the X is chosen randomly and has the equal chance of being selected as any other individual In order for random sampling to work the probabilities must stay constant from one selection to the next meaning you must replace the sample once you ve pulled one This makes it so that it is possible to sample the same X twice but this creates the problem that there are multiple copies of this individual piece of data in your sample What is a normal distribution and how is it related to probability and z scores A normal distribution is a distribution that is symmetrical with the greatest frequency being in the middle when the mean median and mode are all equal to 0 00 and has the standard deviation is 1 00 In standardized distributions probabilities are defined as the proportion of area under the curve The Z score allows us to easily divide up the distribution the smaller side under the curve from x is called the tail while the larger side is called the body Steps to determine probabilities of obtaining specific scores Step 1 sketch distribution identify mean and SD locate X Step 2 Shade portion of distribution you re concerned with Step 3 Estimate proportion in shaded area Step 4 Convert X value into Z score value Step 5 Consult Unit Normal Table to arrive at proportions negative sign doesn t matter in table but must remember to input negative sign later Step 6 Identify whether concerned with body or tail of distribution Step 7 Estimate proportion from Step 4 How do you know if you ve messed up If a proportion is greater than 1 00 or negative you ve messed up Neither of can ever occur Lecture 10 October 1 How to convert X Z P To start off you must convert your X into a Z score using the Z score formula Z X Next refer to your Unit Normal Table and find your Z score in column one Determine if you are analyzing the tail or the body of the distribution and depending on which refer to either column B C or D depending on the question in the UNT to figure out the proportion of your Z score How to convert Z P Refer to your UNT and find your Z score Then determine if the question is asking you to analyze the tail or body of your distribution and refer to that to find your probability How to convert P Z Determine whether your question is talking about the tail or body of your distribution Find your probability score under column B or C of your UNT and look to column A within that row to find the appropriate Z score How to convert P Z X Depending whether your question is regarding the tail or body of the distribution refer to either column B or C in your UNT to find your probability Then look to column A of that row to find the appropriate Z score From there you can convert your Z score into X using X Z What are extremes scores in psychology Extreme scores are any score that is beyond 2 from the mean in either direction In psychology the conventional value that represents an extreme score is 5 that is distributed evenly between the two ends of the distribution These extreme scores have a Z score of at higher than Z 1 96 or lower than Z 1 96 The tail of an extreme score will always have a probability of at most P 0 025 Lecture 11 October 3 What is hypothesis testing and what is the process Hypothesis testing is a statistical method that involves comparing empirically observed sample findings with theoretically expected finding Our observed sample findings are what we see in our sample while our theoretically expressed findings are those we expect to see in the population The different types of hypothesis testing are Z T r 2 chi squared F and ANOVA tests The test used depends on the research question although regardless of which test is used the generic formula remains constant These