Page 1 of 5 In Class Assignment 6 Statistical Significance with Z Scores Hypothesis Testing 6 16 Set 1 Important Concepts Statistically Significant Differences In statistics a result is called significant if it is unlikely to occur by chance A statistically significant difference simply means there is statistical evidence that there is a difference between two or more things If there is a significant difference the two things are different If there is not a significant difference the two things are the same Basically we are comparing things to see if they are different from one another There are two kinds of tests the eyeball test and statistical significance o The eyeball test looking with your eyeballs and seeing if there appears to be a difference This test is pretty much worthless on its own o Statistical significance using tables and or SPSS to determine whether the difference we can observe with our eyeballs is unlikely to have occurred by chance Notes Page 2 of 5 Determining Significance Z Scores There are two methods for determining significance The first method our focus today involves using pre determined thresholds based on z tables that tell us what is is not significant There are lots of different tests For now we will use z scores If the score we are concerned with is outside the threshold s then it is significant If the score we are concerned with is inside the threshold s then it is not significant Determining Significance Z Scores Continued These thresholds are called critical values Critical values change depending on the test we are running z versus t versus F etc They are found in a table in this case a z table For z scores the two values we care about are 1 64 and 1 96 Which we use depends on whether we are using a one tailed or twotailed test You can look these up yourself but I wanted to save you time One tailed there is a direction we are looking for a specific change Two tailed there is no direction we are looking for any change For example let s say we have a z score and are trying to determine whether it is significant We are trying to determine whether this z score is significantly different from the critical value that s the point of the test Thus if our score the z score falls outside of 1 96 two tailed then our z score is statistically significant Conversely if it falls within 1 96 it is not statistically significant Questions 1 6 Notes Different from Significance Level which we will cover next week Page 3 of 5 The Pre Show Hypothesis Testing in a Nutshell In statistics we use experiments to determine whether things are significantly different from one another as previously discussed We generate hypotheses about our experiments before we perform them We always have two hypotheses o Null hypothesis the things we are comparing are not significantly different o Research hypothesis the things we are comparing are significantly different Therefore before pushing our magic statistics buttons we predict that something will happen and that nothing will happen Hypothesis Testing Continued When testing our hypothesis we are interested in proving that the null is false We can only directly prove that something is not true We can never directly prove that something is true If we want to show evidence that something is true you must first assume that it isn t the null hypothesis If we show that this assumption the null is logically impossible then we have indirectly proven that the research hypothesis is true If we prove the null false then we reject the null If we can t prove the null is false then we fail to reject the null Basically in hypothesis testing we hypothesize there is no difference between the things we are comparing If we find that a difference exists then we reject the null Questions 7 12 Notes Page 4 of 5 Set 2 Determine Statistical Significance by Hand Method 1 A psychologist is interested in whether cognitive behavioral therapy CBT affects participant scores on a measure of depression He thinks that people who undergo CBT will have lower depression scores He knows the average mean depression score for the general population is 5 67 The general population has a normal distribution He randomly selects 10 participants from this population and subjects them to cognitive behavioral therapy After treatment the mean score on the same measure of depression for these 10 participants is 4 34 with a standard deviation of 1 37 Step 1 Decide whether the test is one tailed or two tailed and identify the null and research hypotheses Questions 13 15 Step 2 Calculate a z score We need to standardize the score in order to be able to compare two separate groups the population and the sample We do this using z scores but the formula for z scores changes just a little bit Before we learned how to use z scores for a single value Now we need to use the formula for z scores for a sample mean Z Sample Mean Population Mean Standard Deviation Number in Sample o We need to plug the numbers from the problem into the formula Questions 16 19 o Then we need to find the z score for the sample mean Question 20 Step 3 Find the critical value o 1 64 is the critical value for a one tailed z test o 1 96 is the critical value for a two tailed z test Question 21 Step 4 Finish it out o Compare the z score for the sample mean to the critical value Question 22 o Decide whether to reject fail to reject the null Question 23 o Interpret your results Question 24 Notes Denominato r also called Standard Error of the Mean Page 5 of 5 Set 3 Do a Problem Using A Combination of SPSS Calculations By Hand A professor wants to know whether her exams are harder or easier relative to the other professors exams in her department She knows that the average mean exam score for the department is 87 50 and these scores are normally distributed She has 10 students in her class Their exam scores are as follows Questions 25 27 85 92 100 84 80 78 88 84 93 84 Step 1 Set up your dataset o Create a variable for Participant ID and format it correctly o Create a variable for exam scores titled Scores and format it correctly then enter the data Step 2 Find the descriptive information o Analyze Descriptive Statistics Frequencies o Move Scores over o Unclick Display Frequency Tables and click OK o Statistics Mean Median Mode Std Deviation S E Mean The denominator in the z formula we just used is called the Standard Error of the Mean o Continue o Paste o Go to Syntax Highlight Run Questions 28 32 Step 2 Calculate the