T Test Only PDF

Modulus 6: The Single Sample T test Population standard deviation is rarely known, hence cant use z test, we use t test. T test: Uses sample standard deviation as an estimate of population standard deviation - Almost all aspect of z test and t test are the same when conducted - Still use...

Modulus 6: The Single Sample T test Population standard deviation is rarely known, hence cant use z test, we use t test. T test: Uses sample standard deviation as an estimate of population standard deviation - Almost all aspect of z test and t test are the same when conducted - Still use null hypothesis Significance testing - Assign value that indicates no effect to the null hypothesis and proceed assuming null is true - Apply alpha level of 5% and determine probability of our mean occurring- result determines whether null hypothesis is rejected or not Difference about t-distribution S = sample standard deviation/ sample standard error - The critical limit corresponding to the alpha level of 5% will warry not just +/- 1.96 we require the degrees of freedom - T distribution requires we consider sample size and degree of freedom to determine probability if sample mean Degree of freedom - 1.96 will change according to the size of the sample- degrees of freedom are - one less than our sample size for a sample t-test (n-1)- calculate the df then go find in the chart - For the null to be right the probability of getting 94 sample mean would have to be higher than 5% which in this case is not as the sample mean probability was 1.6% Example: Does head injury affect IQ? - Sample 10 people with acquired head injury - Null hypothesis would be that head injury has no effect on IQ - Sample data M= 94.20, S= 6.16, N=10 Questions 1. What type of test could you conduct if you wanted to compare a sample mean with a population mean, but didn't know the population standard deviation -Ans: A single sample t-test. 2. What is the main difference between a z-test and a t-test? - Ans- Z-test are used when the population standard deviation is known, t-test are used when it is unknown. 3. What does the t-distribution require us to consider when determining the probability of the sample mean? Ans- Sample size and degrees of freedom 4. How are degrees of freedom calculated for a single sample t-test? Ans- one less than our sample size 5. Which of the following interpretations of t-scores is correct? - Ans- If the t-score is not extreme for the degrees of freedom, do not reject the null hypothesis Modulus 7: Independent Sample t- test Independent group research design: participants are assigned to, or come(naturally) from, two or more different groups-different conditions Research question: Is there a difference between the groups? If the null is true there is a 0.007% chance of this happening therefore proving the null wrong because the results show a significant difference. If the null is true there is more than 5% chance of this happening therefore providing evidence for the null to be proven- because there is a higher chance of the given results happening under the null- no statistical significance Summary - The appropriate research design for use with an independent samples t-test is an independent groups design - The independent samples t test- assesses if the difference between the two sample means is different to zero or if one sample mean is < or > than the other - JASP output gives descriptives, t-score, p value, effect size, and more - Writing up test results example - Tests if samples come from the same population or not. Question 1. In an independent group's research design,..different participants are used in each group of the design. 2. What is an independent sample t-test used for? - Ans- To assess whether there is a significant difference between the means if two groups 3. What would be the null hypothesis for an independent sample t-test? - Ans- There will be no significant difference between the population means 4. What is a control group? - Ans- A group who does not receive the experimental treatment. Modulus 8: Repeated Measures t- test Repeated measures research design - To assess whether there is a significant difference in participants scores before and after an event/ can be used to compare scores pre- and post-treatment - The samples come from different populations before and after an event - each participant is measure in 2 or more different occasions(eg. Time1, time2/before, after) - Also known as ‘paired samples’ or ‘related samples’ t-test - Research question: eg. Is there a change across time? Modulus 9: Correlation Correlational research design: concerned with a relationship between 2 variables/ associations between 2 variables (e.g. Age and IQ- Do we get smarter as we get older) variable x- x axis, variable y-y axis used scatter plot - Correlation checklist: examines linear and symmetrical assolation - Symmetrical: the relationship between bob and susan is the same as the relationship between susan and bob - Pearson’s r- A measure of correlation in a sample - Q What does a correlation coefficient 0f -0.9 indicate? - A strong weak association - In a negative linear association, as scores on x decrease, scores on y increase -  - 0.940= almost 1 meaning very strong correlation and positive - Null is far less than 0.05 so reject the null - In real research positive correlation is not often seen Summary: - Correlation analysis examines associations between 2 variables - Pearson's r is a measure of correlation in a sample - May be either positive or negative, depending on direction of association (range from -1 to +1)  - Coefficient values close to -1 or +1 indicate stronger association. 0 indicates no association at all. - Can infer from samples to population correlations using standard null hypothesis significance testing - A significant correlation provides evidence for association in the population Modules 6-9 T test M6- Single sample M7- Independent groups W8- repeated measures W9- Correlational Example Questions 1. Do people who listen to kpop have higher IQs than those who do not? Ans: Single sample 2. Is satisfaction with life associated with number of pets Ans: Correlational 3. Do people display faster cognitive reaction times after playing Call of Duty Ans: Repeated measures 4. Do people who drink alcohol more than 4 times a week sleep less than the national average Ans: Single Sample 5. Is amount of caffeine consumes associated with anxiety Ans: Correlational