Notes for 2/23/15-2/25/15
Notes for 2/23/15-2/25/15 PSYC 3301
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This 4 page Class Notes was uploaded by Rachel Marte on Monday March 2, 2015. The Class Notes belongs to PSYC 3301 at University of Houston taught by Dr. Perks in Fall. Since its upload, it has received 122 views. For similar materials see Introduction to Psychological Statistics in Psychlogy at University of Houston.
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Date Created: 03/02/15
22315 amp 225 15 Introduction to Hypothesis Testing Note The same material was covered on both dates 22315 amp 22515 and the same PowerPoint was used so I have compiled both explanations and combined them under the same heading Logic of Hypothesis Testing The entire point of hypothesis testing is to use samples to make inferences about the population We use hypothesis testing when we want to know the likelihood of obtaining the results we got from the sample ie the sample mean from the population We can then compare this probability with a standard e g 5 the most commonly used standards are 05 01 and 001 to determine whether or not these findings are very unlikely to occur in the population If we determine that a sample mean is very unlikely to occur in a certain population e g it has less than a 5 chance of occurring in that population we consider the possibility that that statistic does not in fact come from that population Such unlikely results suggest that the sample mean may actually come from a different distribution which would mean that there is a significant difference between that distribution and the original distribution of the population In other words we are trying to determine whether or not a sample is part of the original distribution or is part of its own distribution If the sample is part of a different distribution then there must be a significant difference between the sample and the original population In this way we can tell if a treatment has a significant effect A hypothesis test is a statistical method that uses sample data to evaluate a hypothesis about a population parameter In order to perform hypothesis tests we will combine what we know about zscores probability and sampling distributions The Process of Hypothesis Testing We follow four steps when performing a hypothesis test 1 State a hypothesis about a population null and alternative hypotheses 2 Use the hypothesis to predict characteristics the sample should have set criteria for a decision on whether or not a sample is significantly different from the population 3 Obtain a random sample from the population 4 Compare the obtained sample to the prediction about the population The Hypotheses As stated above the first step in performing a hypothesis test is to formulate the hypotheses we want to test We always state two hypotheses one for each possible outcome The hypotheses 1 The null hypothesis Ho treatment has no effect there is no change or relationship present there is no difference between the population and sample mean they come from the same distribution 2 The alternative hypothesis H1 or Ha treatment has an effect on the dependent variable there is an effect come from a different distribution We state the null and alternative hypotheses each time we perform a hypothesis test We work off the basis of falsification so we can never prove a hypothesis The results of the hypothesis test will allow us to support one hypothesis and reject the other but we can never say that we have proved a hypothesis to be true The null hypothesis simply states that there is no difference between the population mean and sample mean but the alternative hypothesis can take a couple different forms depending on whether or not we are performing a onetailed or twotailed test We use a twotailed test when we simply want to know whether or not there is a difference between the population mean and sample mean but we do not care what the difference is ie whether or not the sample mean is significantly higher or lower than the population We can also perform directional hypothesis tests if we want to know what direction the difference is in We use a positive onetailed test if we want to know whether or not the sample mean is significantly higher than the population mean e g Does studying for statistics tests significantly improve students grades We use a negative onetailed test if we want to know whether or not the sample mean is significantly lower than the population mean e g Does drinking signi cantly impair students driving abilities The shaded region of each graph shows where on the distribution E we expect the sample mean to 1 fall or which end of the pt39xlti c nzlr Ult l its distribution we are testing for significance For example in a positive one tailed distribution uni i we are interested in whether or 39c 39lil Ollc Llllt x l l39x l not the sample mean falls on the far right end of the distribution and if it is high enough to be i significant Two tazlcd test We can state the hypotheses verbally in sentence form or we can symbolize them mathematically The null hypothesis is symbolized pretty much the same way every time but how we state the alternative hypothesis depends on whether or not we are using a onetailed or twotailed test and what direction we re testing if it s a onetailed test How to state the hypotheses 1 The null hypothesis 0 Sentence form e g There is no difference between the sample mean and the population mean 0 Symbolization o Hmiu or O Hoip0 2 The alternative hypothesis a Twotailed test 0 Sentence form e g There is a difference between the sample mean and the population mean 0 Symbolization o Huiiu or O H1ip 0 b Positive onetailed test 0 Sentence form e g The sample mean is significantly higher than the population mean 0 Symbolization o Huigtu m o Huiugt0 c Negative onetailed test 0 Sentence form e g The sample mean is significantly lower than the population mean 0 Symbolization o H iltu or 0 H1 2 u lt 0 The distribution of sample means if the null hypothesis is true all the possible outcomes Sample means close to H0 hlghprobabllily values if H0 is true Extreme Iow u from HD Extreme low prOPObIUW VOerS probablllty values If l lO Is true If HEI is true Basically what our hypothesis is saying is that if our data is in the ends i e very unlikely to occur low probability of occurring then it is not likely that our null hypothesis is true In other words it is likely that our sample is from another distribution
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