Scales of Measurement
What is a nominal variable?
It is qualitative and discrete in nature. It is a categorical variable that is exhaustive and mutually exclusive.
(It can be dichotomous if there are only two answer choices (e.g., yes/no)).
What are the measures of central tendency?
Mean, Median, Mode
What is the outline of the null hypothesis symbolically and verbally?
Symbolically:
H0: Mu2=Mu1 OR H0: Mu2=[Benchmark value]
Verbally:
There is no difference between [population 2] and [population 1] in terms of [variable of interest].
What is the outline of the null hypothesis symbolically and verbally?
Symbolically:
H0: Mu2=Mu1 OR H0: Mu2=[Benchmark value]
Verbally:
There is no difference between [population 2] and [population 1] in terms of [variable of interest].
Using the z-table, what is the probability of a value falling below the z-score?
z-score: -3.44
0.001
Tell me what a nominal variable is, how we determine it is nominal, and an example of a nominal variable.
A nominal variable is a categorical variable that is exhaustive and mutually exclusive. It can be dichotomous depending on the quantity of answer choices (e.g., yes/no). It is also qualitative and discrete.
To determine if it is nominal, there must be an indication of categories or no possibilities of numerical rankings.
Examples may vary.
What are the measures of dispersion?
Range, Variance, Standard Deviation
What is the outline of the alternative hypothesis?
Symbolically:
HA: Mu2≠Mu1 OR HA: Mu2≠[Benchmark value]
Verbally:
There is a difference between [population 2] and [population 1] in terms of [variable of interest].
What is the outline of the alternative hypothesis?
Symbolically:
HA: Mu2≠Mu1 OR HA: Mu2≠[Benchmark value]
Verbally:
There is a difference between [population 2] and [population 1] in terms of [variable of interest].
Using the z-table, what is the probability of a value falling above the z-score?
z-score:1.67
0.048
Tell me what an ordinal variable is, how we determine it is ordinal, and an example of an ordinal variable.
An ordinal variable is rank ordered with unknown distinctions of the distances between the rankings. This variable is also qualitative and discrete.
To determine if it is ordinal, there must be a clear indication of ranking, however no clear indication of the distance between each ranking.
Examples may vary.
What are the distribution shapes determined by?
Skewness and Kurtosis
We randomly sampled 30 ballparks in United States to see how many pints of beer they sold between 7th and 8th inning on Opening Day in 2024. We want to compare our sample to the national average in 2020 μ2020 = 162 pints (SE = 7.66).
What test are we conducting? How do you know?
We are conducting a z-test.
Population variance is known and there is a comparison being made between two groups.
In 2023 the national survey of health attitudes collected information on the health attitudes and beliefs from approximately 7100 randomly selected Americans. One of the variables in this survey asks Americans how important religion is to them. Answer classes for this variable are on a 5-point Likert scale anchored by 1(not at all important) to 5(very important). In 1985 a random sample of Americans determined that the average American had an importance of religion score of 4.01. you want to know whether our 2023 sample is different than the u.s. in 1985.
What test are we conducting? How do you know?
We are conducting a Single Sample T-Test
Population variance is not known and there is a comparison being made between two groups.
Using the z-table, what is the probability of a value falling below the z-score?
z-score:-2.33
0.010
Find the variable mathattitude. This variable is a composite variable created by averaging up the individual scores on each of the four SemanticDif variables. These variables are meant to access student attitudes toward math, wherein low values (1) represent positive attitudes toward math and high values (5) represent negative attitudes toward math. What scale of measurement is the variable? How do you know?
Mathattitude is an Interval variable.
As determined, it is an ordered numerical ranking of math attitudes. It indicates the differences between each measuring point and is also quantitative/continuous. As the blurb mentions math attitude was measured from 1 (positive attitudes) - 5 (negative attitudes), we know that there is no true zero and would be deemed as an interval variable.
Find the variable mathattitude. This variable is a composite variable created by averaging up the individual scores on each of the four SemanticDif variables. These variables are meant to access student attitudes toward math, wherein low values (1) represent positive attitudes toward math and high values (5) represent negative attitudes toward math. Please interpret all valid descriptive statistics for this variable. (You do not need SPSS to give me an outline)
Mean: The average answer/score was...
Median: 50% of the sample scored below ___ and 50% of the population scored above.
Mode: The most frequent answer was ...
Standard Deviation: The average distance to the mean is...
Skewness: The skewness of .... indicates that the variable is symmetrical/asymmetrical.
Kurtosis: The kurtosis of .... indicates that the variable is bell-shaped/not bell-shaped.
We randomly sampled 30 ballparks in United States to see how many pints of beer they sold between 7th and 8th inning on Opening Day in 2024. We want to compare our sample to the national average in 2020 μ2020 = 162 pints (SE = 7.66).
What are the assumptions for this test and interpret the assumptions utilizing the blurb.
1. Observations are independent: One ball park cannot affect the beer intake of another
2. Randomly sampled: as stated in the blurb
3. Normally distributed: There is a sample population of 30 ballparks.
4. Population variance is known: As stated in the blurb, we know our standard error is identified.
In 2023 the national survey of health attitudes collected information on the health attitudes and beliefs from approximately 7100 randomly selected Americans. One of the variables in this survey asks Americans how important religion is to them. Answer classes for this variable are on a 5-point Likert scale anchored by 1(not at all important) to 5(very important). In 1985 a random sample of Americans determined that the average American had an importance of religion score of 4.01. you want to know whether our 2023 sample is different than the u.s. in 1985.
What are the assumptions for this test and interpret the assumptions utilizing the blurb.
1. Observations are independent: LGBT folks scores do not affect Americans scores.
2. Random Sampling: As stated in the blurb
3. Normally distributed: The sample population is n=7100, deeming it normally distributed. (n<30)
(HINT: You also know the benchmark value but not the SE).
Using the z-table, what is the probability of a value falling below the z-score?
z-score:0.99
0.839
Find the variable mathanxiety. This variable is a composite variable created by summing up the individual scores on each of the five Math_Anxiety variables from 0 not at all- 5 very anxious. What scale of measurement is the variable? How do you know?
Math_Anxiety is a Ratio variable.
As determined, it is an ordered numerical ranking of anxiety. It indicates the differences between each measuring point and has a true zero. It is also quantitative/continuous. As the blurb states the measurements of 0 (not at all) - 5 (very anxious), we know that there is a true zero furthermore solidifying that it is a ratio variable.
Find the variable mathanxiety. This variable is a composite variable created by summing up the individual scores on each of the five Math_Anxiety variables from 0 not at all- 5 very anxious. Please interpret all valid descriptive statistics for this variable.(You do not need SPSS to give me an outline)
Mean: The average answer/score was...
Median: 50% of the sample scored below ___ and 50% of the population scored above.
Mode: The most frequent answer was ...
Standard Deviation: The average distance to the mean is...
Skewness: The skewness of .... indicates that the variable is symmetrical/asymmetrical.
Kurtosis: The kurtosis of .... indicates that the variable is bell-shaped/not bell-shaped.
Please give me the outline of the conclusion for a z-test.
Our sample of [insert sample description] has a test statistic of z= [z-score], with a p-value of p= [p-value]. Since our p-value is [less than/greater than] our chosen alpha of a= 0.05, we will [reject/fail] to reject the null hypothesis that states [insert verbal null] and find support for our research hypothesis that states [insert verbal alternative].
Please give me the outline of the conclusion for a single sample t-test with the 95% confidence interval.
Our sample of [insert sample description] has a test statistic of t([df])= [t-score], with a p-value of p= [p-value]. Since our p-value is [greater than/less than] our chosen alpha of a= 0.05, we [reject/fail to reject] the Null Hypothesis that states [insert verbal null].
We can be 95% certain that our current sample comes from a population that is [lower] to [upper] [units] [above/below] the benchmark of [benchmark value].
Using the z-table, what is the probability of a value falling above the z-score?
z-score: -0.67
0.749