Second Midterm PMAP 4041
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What are the differences between nominal, ordinal, and interval level variables?
- Ordinal and Interval level variables both can be RANKED..
- Nominal level variables cannot be ordered
- Ordinal level variables cannot be measured.
Describe the difference between independent and dependent variables and give an example.
Independent variables are a CAUSE of the dependent variables. For example, political parry affiliation is an independent variable because it has an EFFECT on how one feels about abortion, the dependent variable.
What values does Gamma take on and how are they explained?
Gamma takes on the values between -1 and 1. They measure the magnitude of the realtionship in saying that numbers closer to 1 are strong, while numbers closer to 0 are weak.
What does the chi squared statistic (x2) do and what do we assume from it?
It measures how far a sample is from what we expect to see in a random sample from a population with NO relationship. If x2 is too far from what we expected, we can conclude that the sample did not come from a population with NO relationship and therefore conclude that the variables must be related in the popualtion.
What is the difference between the null hypothesis and the alternative, or research hypothesis?
- The null hypothesis (H0) states that there is NO relationship between the variables in the population
- The research hypothesis (H1) states that there IS a relationship between the variables in the population
Describe the reasoning behind a critical value.
Critical values are where the rows and columns meet (degrees of freedom and significance level). These values show that if the null hypothesis is true, there is a (25%, 10% or 5%) probability that x2 will be greater than 1.32, etc. etc. If null hypothesis is NOT TRUE, then we have no idea what those probabilities are except that they are higher.
What is the golden rule of rejecting and accepting the null hypothesis?
- Do not reject H0 when x2 is less than X?
- Reject H0 when x2 is greater than X?. This is the shaded area to the right of the critical value of the graph and is usually called the "rejection region"
What are the steps in the hypothesis test?
- 1. State the research and null hypothesis
- 2. determine the sampling distribution for the test statistic if null hypothesis is true
- 3. Choose the significance level and determine appropriate decision rule- the accepted probablity of making a Type 1 Error
- 4. Calculate the test statistic (x2)- ((O-E)2/E))1, ((O-E)/E))2,...
- 5. Reach a conclusion- if x2 is larger than the test statistic, then reject the null. If less, you do not have enough evidence to conclude relation between variables.
What is the correct answer forming for the conclusion of a Test Hypothesis Statistic?
20.27 is greater than the critical value. At 5% level of significance, the value of the test statistic is greater than the critical. Therefore, we can reject the critical value
What is the importance of stating the degrees of freedom for a distribution like x2?
Until you know the degrees of freedom, we cannot pinpoint the exact chi squared distribution
What is the first step in doing a statistical hypothesis test?
Define the null hypothesis and the research hypothesis
What is the purpose of scatter plots?
They show the relationship of interval level plots
"For the 5% level of significance the critical value for the x2 distribution with13 degrees of freedom is 22.36. In terms of the x2 distribution's PDF what does this statement mean?
The area under the chi squared 13 PDF to the right of 22.36 is 5%.
Break down the Bivariate Regression formula.
- Y-hat= dependent variable; the expected value when x=0; value is determined by the equation
- a= constant; usually calculated by computer
- b= regression/slope coefficient; the expected change in y for a one-unit increase in x
- x= independent variable; you can choose this value
What is the difference between the reference group and the named group? How do they relate to the regression coefficient (b)?
- The reference group is the group that has the value 0 for the independent variable
- The named group is the group that has the value 1 for the independent variable
- The regression coefficient represents the difference in mean values of y between the named group and the reference group
Explain the correlation coefficient.
- It measures strength and direction of a relationship, just like Gamma
- The closer a value is to 0, the weaker the relationship
- The sign of the relationship indicates whether the relationship is positive or negative
Which variables are shown on a scatterplot and where exactly do they fall?
- the independent variables (x) values are graphed on the horizontal axis
- the dependent variables (y) values are graphed on the vertical axis
How do you find the median of a set of observations?
- Add 1 to the # of observations and divide by 2 ((n+1)/2)th
- The median will be the ___th observation
- In the case of an even # of observations, average the observations and the result will be the median.
- DO NOT COUNT THE TOTAL OR NO ANSWER AS OBSERVATIONS!!!
How do you calculate the variance and standard deviation in a set of grouped data?
- subtract the mean from each observational value (Xi-X)
- square all of the values from there (Xi-X)2
- add all of the squared values up =sum(Xi-X)1+(Xi-X)2+....
- divide the sum by the #of values(n) minus one (n/(n-1))
- To calculate the standard deviation, take the square root of the variance.
Which measure of central tendency would work best for each type of variable?
- nominal = mode, frequency distributions
- ordinal = median, frequency distributions
- interval = mean, median (sometimes), standard deviation
What do the critical values explain?
- If the null hypothesis is true (if there is no relationship in the population from which the sample is drawn), there is a __% probability that X2(critical value) will be greater than the test hypothesis value of __.
- IF AND ONLY IF THE NULL HYPOTHESIS IS TRUE!!!
What is the decision rule of accepting and rejecting the hypothesis?
- accept Ho whenever the X2 (critical value) is LESS than X?2
- reject Ho whenever X2 (critical value) is GREATER tthan X?2
How do you find the percentage of those who believe Iran's nuclear program is a major threat that are Democrats?
- Divide the # of Democrat respondents who believe the program is a major threat by the total # of respondents who believe the program is a major threat
- Multiply by 100 to make a percent
How do you find out the number of respondents who believe the nuclear program is a minor threat are Republican?
Multiply the total # of respondents who believe the program is a minor threat by the % (in decimal form) of respondents within the nuclear program who believe it is a minor threat that are Republican (135*0.207)= 28
Who does the third row in a crosstabulation reference to?
It tells "__ % of ___ (in the dataset) think that Iran's nuclear Program is a major threat to the USA.
What does the second row of a crosstabulation tell us?
It tells us that "__% of those who think Iran's Nuclear Program is a major threat to USA are ___.
What does the fourth row tell us?
It tells us that "__% of the entire dataset are ___ who also think that Iran's Nuclear Program is not a threat to the USA.
How do you calculate the cumulative frequency and cumulative percents in a frequency table?
You consecutively add up every frequency and percent after each other .
How do you calculate the valid percents in a frequency table?
- you divide the percent (frequency/10) by the total percent (NOT INCLUDING MISSING VALUES)
- multiply by 100
Interpret the value of Gamma (0.229)
The association between the two variables is weakly positive. The higher (or lower) values of the independent variable are closely assiciated with the higher (or lower) variables of the dependent variable.
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