Inquiring Minds Part 2

Inquiring Minds – Part 2 Question Response What is a T-Test? A t-test is a significance test that compares 2 groups (data about the groups is interval ratio) The relationship is significant if the change of occurring at RANDOM is .05 or less.

What does a t-test For example, assume I have 28 PLS 205 exam scores and the average score do? for the female students is 88.8 while the average score for the male students is 82. Is the difference (88.8- 82 = 5.2) between these two groups due to random error or is there a statistically significant disparity in PLS 205 ability based on whether the test-taker is male or female?

The t-test accounts for the “mean difference” (5.2) AND the standard deviations or variability of scores among males versus females. Typically when the mean score is relatively high (big difference between the first group and the second group) AND the variability is relatively small for the two groups-- the t-test will find the groups are statistically significantly with a sig. = .05 or less.

How do you read a The output from a “t” will typically include: the computed t-value; degrees t-test? of freedom and significance. The “t”value does not tell the reader anything in particular, however the larger the t-value typically the more significant What are the the relationship. important numbers on a t-test? Degrees of freedom are the number of items included in the computation (e.g. 28 students in the example above) -2. Comparing men and women’s What are we scores for 28 PLS 205 students would mean 28-2 or 26 degrees of freedom. comparing? The significance can be from .0000 to 1. Something is significant in the How does a t-test social sciences if it happens --at random --less than 5 times in 100 or =.05 or work? less.

What is the The purpose is to indicate if two groups are really different or if their purpose of the t- differences are due to bias. For example are math scores of men and women test? When do you due to random differences OR does gender introduce a bias that might use it? systematically account for differences in scores? The t-test can indicate if the difference is really a difference or not. When your data is interval/ratio and you want to test if two GROUPS are different or really the same, you use a t-test.

What is the A t-test is a significance test –similar to Chi Square. It tries to determine if difference between events are random? A PRE test determined if knowing about an a t-test and PRE? independent variable, e.g. level of education, allows me to reduce the number of errors I make regarding the number of months of unemployment a person may experiences. PRE tests are Kendall’s tau, Gamma, R2 What is an An ANOVA operates like a t-test BUT allows you to compare more than 2 ANOVA (the groups. Let’s say for the same 28 students I can identify those who are whole thing) ? Democrats, Republicans and Independents. Now I have three means and three measures of variation.

How does it work? Are the average differences between Democrats, Republicans and Independents test scores GREATER than the variations among Democrats, Republicans and Independents? When the differences are significantly greater then the ANOVA, will have a sig. = .05 or less. The ANOVA –like the t-test—is a significance test trying to determine if the differences between groups are due to random error or not.

What is an F An F-score is the computed value for an ANOVA. score? What is a A Pearson’s correlation is a formula that tries to determine how much Pearson’s “corresponding” response one gets with each additional unit of input one correlation? (r or applies. R)

What is Assume I have an eyedropper of steroids and I feed the drug to some white correlation? mice who are then encouraged to jump up a wall. Without steroids the mice will not jump up the wall. However, with one drop of steroids the mice jump 1 inch but with 2 drops the mice jump 5 inches. The correlation seems to be strong – about .88. A perfect correlation would be 1. Every drop has an equal and corresponding influence on the jumping score of the mice. A weak correlation would be .002. For every corresponding drop of steroids there is barely a noticeable change in the mice jumping behavior.

What is R2? Since r is the size of the impact of one variable on another (see information What is R2 versus above), then R2 is how much of the relationship is EXPLAINED by “r”? knowing this relationship.

If your r =1 then R2 =100% or you can explain everything. You are omnipotent, a supreme power. On the other hand if the r =.05; the r2= .0025 and you know only 2 tenths of 1,000ths of what you knew initially and your

increased wisdom is very small.

What exactly is Unstandardized coefficients are beta weights or “slope” values for a line the difference that are computed from the raw data. between standardized Standardized coefficients are beta weights or slopes derived by translating coefficients and the raw data in z-scores and then computing the slope of the line. unstandardized coefficients? What is a Beta? A beta is a coefficient or the weight one variable (interval/ratio) has on another. In a regression formula the “betas” are the coefficient values of the What are the INDEPENDENT variable (s) used to determine the effect on the dependent model summary variable. and its components? For example, I have a regression line to estimate how much weight a teen

will: Ygained in pounds = 10 + 2X fast food. What is it used for? Then, I can estimate (all other things being equal) that if the teen typically eats 5 fast food meals a week he/she will gain 20 pounds a month or 10 + 2 How can we use (5) = 20. In this example “2” is the beta or weight applied to the behavior regression to (fast food meal eating) which influences the weight gained. If the teen eats predict? “0” fast food meals then the anticipated weight gain is = 10 + 2 x 0 or 10 +0 =10.

The equation for Once the data has produced a “line of best fit” then any number can be unstandardized plugged into the model of Y= Constant + Beta X independent variable … to estimate coefficients is the consequence for a specific case. For example, estimate the number of multiplied by fast food meals you eat each week for any meal (breakfast, snack, lunch or what? Where do diner) and place that number into the formula Ygained in pounds = 10 +2 X fast food. you get the It will provide an estimate gain. It may not be your gain because of your numbers? age, metabolism, gender, health, level of activity BUT if fast food were the only factor then it would be a reasonable guess about your weight gain – all other things being equal.

What are the The equations for the coefficients are found in Powermutt page 100. equations for the coefficients? What is There is no single regression. There is linear regression where a single regression? What independent variable (that is interval/ratio) varies. The researcher seeks to is single see if changes in the independent have a noticeable effect on the dependent regression? What which is also interval/ratio. For example if I vary the intake of alcohol is linear (measured in ounces) what effect will it have on response times of drivers regression? (measured in seconds). The pattern is that as alcohol increases the response time decreases. The line that represents this single, simple relationship is the regression line. The slope of this line will be negative (-) in this case.

What is multiple Multiple regression is when there are 2 or more independent variables used regression? to determine the effect on the dependent variable. In the example above if the researcher added “years of driving experience” to the analysis then the dependent variable is still “response time” but the multiple independent variables are now alcohol in ounces and experience in years.

What are Let’s assume that Sally is 5 feet and 100 pounds (5, 100 on a graph). She is residuals? one of 100 people in a study. Based on Sally and the other 99 respondents a regression line is developed. The regression line estimates that a 5 foot person would weight 108 pounds (5,108). The residual is the distance between Sally’s point (5,100) and the estimated point (5,108). How do you read a To interpret a linear regression you need to look at: linear regression? R = correlation between the independent and dependent variables R2= how much changes in the independent variable explain changes in the What are the steps dependent variable for analyzing Y= Constant + Beta X independent variable for the raw data which represent is regression represented by the “unstandardized coefficients” and models? Yest. = Beta X independent variable for the standardized coefficients, and t = to indicate if the raw points are close to the estimated line or really far How do you away. (see page 99-102) interpret the model?

What is the The purpose is to make a model of the relationship that will help you predict purpose? When what will happen. Assume I have a new steroid drug and want to know its do you use it? effect on athletes. I run a serious of tests and find that as the dose increases persons are able to run faster and jump higher. Also, I find that when persons stop taking the drug their immune systems weaken, they get headaches, viruses and backaches. By modeling the dosages to the consequences I can fine tune how much of the drug can be safely given, In fact drug policies are largely regression analysis that indicates to physicians what condition (diagnosis), for what gender, by weight and age a drug may be used. We use regression in determining the best use of money to influence outcomes. For example how much should the Fed reduce the interest rates to stimulate spending or how many hours of schooling per year should children complete to become proficient at their grade level, etc.

What is the Y= Constant + Beta X first independent variable + Beta X second independent variable … formula multiple regression? What are Z Z scores are values under a curve. By assigning a raw score a “Z” score you scores? are able to compare items more accurately. For example, while in Germany you are paid in Euros along with Fritz. How comparable is his pay to yours? Money fluctuates from day to day in value so it may be greater or smaller depending on currency trading. However, one can convert the number into where each pay amount is expressed as a Z score. Now you can compare your pay with Fritz on a standardized system not subject to the vagaries of currency markets. What is The GSS and ANES surveys have been conducted for over 40 years and longitudinal since the data stretches over a long period of time, we can analyze the analysis? similarities and differences among generations. You and your parents may have similar preferences regarding political candidates but very different desires regarding music. If I want to compare your generation’s preference for political candidates with that of your parents and grandparents -- I recode the age data by generation and see how a line chart displays the generational output.

If generation lines overlap and intersect then generation differences are not significant and unimportant. However, if the lines are parallel then they are apt to be significant and represent important differences.