Scales
What are the SCALES of measurement (Hint: There's 4)
Nominal, Ordinal, Interval, Ratio
What is the variable that is manipulated by the researcher?
Independent variable
What is mean, median, and mode?
Mean: average of a set of numbers
Median: the middle number when your data is arranged from smallest to largest (50th percentile)
Mode: the number that appears the most times in your data set
Although research questions typically concern a ________, a research study typically examines a __________.
A. parameter, population
B. sample, population
C. statistic, sample
D. population, sample
D. population, sample
What are the real limits of the class interval 15-19, assuming the scores are measuring a continuous variable?
14.5 - 19.4
The teacher in a communications class asks students to identify their favorite reality television show. The different television shows make up a ________ scale of measurement.
nominal
What is the variable that is observed to assess the effect of the treatment?
Dependent variable
Advantages and Disadvantages of Mode
Advantages:
- easy to compute
- simplest to interpret
- calculated for any scale of data
Disadvantages:
- ignores most of the information in the data
- sample mode is not good estimate for population mode
A researcher is interested in the effect of caffeine on memory for a population of students at HPU. If an average memory score could be obtained for all of the students, it would be an example of a __________.
A. sample
B. statistic
C. population
D. parameter
D. Parameter
Parameter = a value, usually a numerical value, that describes a population
______ summarize and describe the data in a sample while ______ are used to make educated guesses about the population
A. Distributions, descriptive stats procedures
B. Inferential stats procedures, descriptive stats procedures
C. Descriptive stats procedures, inferential stats procedures
D. Inferential procedures, ordering and grouping of data
C. Descriptive stats procedures, inferential stats procedures
The number of pets each coworker reports having would be on a(n) _________ scale of measurement.
Ratio
A scientist wants to test how the amount of sunlight affects the growth of tomato plants. She places 20 tomato plants in identical pots with the same soil and water. She puts 5 plants in full sun, 5 in partial shade, 5 in mostly shade, and 5 in full shade. After 4 weeks, she measures the height of each plant. What is the independent variable in this experiment?
A. The amount of sunlight each group receives
B. The type of soil used
C. The height of the tomato plants
D. The number of tomato plants in each group
A. The amount of sunlight each group receives
What are the advantages and disadvantages of the median?
Advantages:
- not sensitive to outliers/skewed data
- can be used for ordinal, interval, or ratio data
Disadvantages:
- not a reliable estimate for the population median
Sampling error is the naturally occurring difference that exists between a sample statistic and the corresponding population parameter.
The ACT writing score of entering college freshman is an example of a(n) ________ scale of measurement.
Interval
A teacher wants to find out if the amount of time students spend studying affects their test scores. She divides her class into three groups: Group A studies for 30 minutes, Group B studies for 60 minutes, and Group C studies for 90 minutes. All students then take the same test, and the teacher records each student's score. What is the dependent variable in this experiment?
A. The number of students in each group
B. The amount of study time assigned to each group
C. The subject being studied
D. The test scores of the students
D. The test scores of the students
Advantages and Disadvantages of the Mean
Advantages:
- uses all data for the calculation
- useful in other calculations (example: hypothesis testing)
- When the sample mean is calculated from a random sample, it is an unbiased estimate for the population mean
Disadvantages:
- sensitive to outliers (skewed data)
- can only be calculated with interval or ratio
A. symmetrical
B. positively skewed
C. negatively skewed
D. cannot be determined
C. Negatively skewed
Describe all four scales of measurement.
Nominal Scale: Just names or categories — no order, no math. (e.g., eye color, gender)
Ordinal Scale: Categories with a ranked order, but the gaps between them aren't equal. (e.g., 1st, 2nd, 3rd place)
Interval Scale: Ordered, evenly spaced numbers — but zero doesn't mean "none." (e.g., temperature in °F — 0° isn't "no temperature")
Ratio Scale: Like interval, but zero really means zero — so ratios make sense. (e.g., weight — 0 lbs means no weight, and 10 lbs is twice 5 lbs)
Which of the following is an example of a continuous variable?
A. the weight of the newborn children in a hospital
B. the gender of each student in a psych class
C. the number of females in each course offered by the university
D. the number of children in a family
A. The weight of the newborn children in a hospital
Why do we need multiple standard methods for defining and measuring central tendency, rather than just one? Give an example of a scenario where each method would be the best choice to use.
No single measure works well for every kind of data.
Mean (average) is most preferred generally and preferred with roughly symmetrical, interval/ratio data
Median (middle of data) is preferred with skewed data or outliers or ordinal data
Mode (most frequent) is preferred with nominal/categorical data, or when you want the most common value
If the same formula were used to calculate both population variance and sample variance, why would sample variance fail to be an unbiased estimator of population variance? What change is needed to make sample variance an unbiased estimator?
The sample mean is calculated from the sample, so it fits that sample better than the true population mean would. This makes squared deviations too small, so dividing by n underestimates the real population variance.
Divide by n − 1 instead of n. This slightly increases the result, correcting the underestimate and making it an unbiased estimator.