Research Methods and Statistics

What is the difference between experimental and quasi-experimental design?

Experimental design involves random assignment which experimenters have more control over; quasi-experimental design is used in real-world settings which essentially limits experimenters' control over the causal relationship

What is correlational design used for and what sets it apart from experimental design?

To measure the strength and direction of relationships between variables as they naturally occur; no manipulation involved.

What is survey design used for?

To gather data from a sample with an aim to describe the characterisics of a larger population

What is the key difference between longitudinal and cross-sectional design?

Longitudinal involves studying the same group over extended periods of time to assess developments, stability, and other long-term effects; cross-sectional involves studying distinct groups to capture a snapshot of a phenomenon.

What is the act of assigning numbers or symbols to characterize things?

Measurement

What do you call the collective influence of factors beyond what is specifically being measured by the test?

Error

System of rules to represent things with numbers to show how much of something they have

Scale

What is the difference between continuous and discrete scale?

Continuous scale can be broken apart more precisely and infinitely; discrete scales do not have in-between values, most of the time only involving whole numbers.

What are the three properties of a scale?

Magnitude (moreness), equal interval (consistent gaps), ratio (absence of a property)

What are different levels of scales of measurement?

Nominal, ordinal, interval, and ratio

Nominal: ; Ordinal:

Description; rank

Interval: ; Ratio:

Equal interval + no true point zero; equal interval + true point zero

What is considered the strongest scale of measurement and why?

Ratio; has all the properties from interval down to nominal + true point zero, allowing to make comparison with less limitations.

What is the goal of descriptive statistics?

To summarize and describe to gain insights into its distribution, shape, variability.

What is the purpose of frequency distribution?

It shows the pattern and spread of scores; how much a score occurs in a distribution.

What is the difference between simple FD and grouped FD?

Simple FD involves using scores as they are and then finding which occurs most frequently; grouped FD involves grouping scores into class intervals to in replacement to actual test scores.

When do we use simple FD?

When dataset is small (n<30) with not many different scores

When do we use grouped FD?

When dataset is large (n>30) or scores are really spread out

What is the difference between bar graph and histogram?

Histograms are used for continuous numerical data to show shape, central tendency, and spread with connected bars; bar graphs are used for distinct categorical groups, with spaces in between.

What are pie charts used for?

To present categorical parts of a whole.

What are scatter plots used for?

To present relationship between two numerical variables.

What are line graphs used for?

To present trends over time.

How does box plot differ from histogram and bar graph?

Used to present minimum, maximum median, quartiles, and outliers as well as to discern if data is skewed or balanced.

How does box plot differ from scatter plot?

Used to show the spread of only one variable as compared to a scatter plot that involves 2 or more.

Another term for box plots?

Box-and-whisker plots

What is the summary of measure that shows where most of the data clumps together?

Measure of Central Tendency

What is considered the most stable and useful measure of central tendency?

Mean

It is equal to the sum of the distribution divided by the number of observations.

Mean

Mean is used for _ and _ data as well as in normal distribution.

Interval; ratio

What is the middle score in the distribution?

Median

If interval/ratio data is skewed, we use __.

Median

Median is especially useful for _ distribution because _

Skewed; it isn't affected by high or low scores (or essentially outliers) unlike the mean.

What is the most frequently occuring score in a distribution of scores?

Mode

Mode is used for __ data.

Nominal

What is the summary of measure that shows how spread out scores are in a distribution?

Measure of Variability

What are the measures of variability?

Range, interquartile range and semi-interquartile range, average deviation, standard deviation, and variance

What do you call the difference between the highest and lowest score in the distribution?

Range

What do you call the difference between Q3 and Q1?

Interquartile range

What do you call the difference between Q3 and Q1 divided by 2?

Semi-interquartile range

What is the difference between quarter and quartiles?

Quarter is the interval; quartiles are the dividing points.

In a perfectly symmetrical distribution, Q1 and Q3 will have __.

The same distance from the median.

Median is equivalent to which quartile?

Q2

What is the difference between average deviation and standard deviation?

Average deviation tells the average distance of each score from the mean while treating both negative and positive signs as positive; standard deviation does the same thing but squares negative numbers to make it positive and then taking its square root to arrive at the SD

How do we calculate the average deviation?

(1) Measure the distance of each score from the mean while treating all scores as positive regardless (2) Sum all the differences (3) Divide them by the number of observations/total number of scores

What is the relationship between standard deviation and variance?

SD is the square root of the variance; variance is SD in squared units

What do you call the distance between each score and the mean?

Deviation score

How do we calculate the variance?

(1) Square the deviation scores (2) Sum them all up (3) Divide by the number of observations/total number of scores

How do we calculate the SD?

(1) Take the square root of the variance

When do we use n-1 in our calculation?

When we're using a sample instead of the population

What are the four measures of location?

Percentile, percentage, quartile, decile

What is the difference between percentile and percentage?

Percentile tells us the position or rank of a person among other testtakers; percentage is a conversion we use to better compare scores

What is n+1 in the calculation of quartile and decile used for?

Serves as a placeholder or imaginary point at the end to make division more consistent

What do you call the degree of asymmetry in a distribution?

Skewness

What is the key difference between positive and negative skewness?

Positive skewness: more scores at the left-negative side, right-tailed; negative skewness: more scores at the right-positive side, meaning left-tailed.

Positive skewness: _ tailed; Negative skewness: _ tailed

Right; left

The test was too difficult if the skewness is __.

Positive

The test was too easy if the skewness is __.

Negative

If the mean, median, mode are all the same, it has __ distribution.

Symmetrical

The peak of the slope/curve is the __.

Mode

The middle ground is the __.

Median

When mean is the greater than the median and mode, the skewness would be __.

Positive

When mean is less than the median and mode, the skewness would be __.

Negative

Explain positive skewness work in relation to the measures of CT.

Mean increases as it is affected by the high score outliers, stretching out the tail towards the high end.

Explain negative skewness work in relation to the measures of CT.

Mean decreases as it is affected by the low score outliers, stretching out the tail towards the low end.

What is the univariate of skewness?

-3 to +3

What is the univariate of kurtosis?

-10 to +10

It refers to the tailedness and steepness of a distribution.

Kurtosis

If normal, the upper and lower __% would be considered the boundary line.

27

If platykurtic, the upper and lower __% would be considered the boundary line.

33

Why is the platykurtic boundary line different from the normal one?

Because the data is more widespread towards the extremes, thus needing to extend to get a similarly representative slice.

What is the difference between the types of kurtosis?

Platykurtic: flat, thin-tailed; Mesokurtic: mid-tailed; Leptokurtic: peaked, fat-tailed

If outliers are infrequent, it is ; If outliers are prominent, it is .

Platykurtic; leptokurtic

Another terms for the normal curve.

Gaussian curve

The first to refer the curve as the normal curve.

Karl Pearson

Who was the first two people who developed the concept of the curve in the early 18th century?

Abraham DeMoivre and Marquis de Laplace

Who had made substantial contributions in the concept of the curve during the 19th century?

Karl Friedrich Gauss

The tail of a normal curve is at __.

2 and 3 SD above and below the mean.

Approximately __% occur between the mean and 1 SD above/below the mean.

34

Approximately __% occur between the mean and ±1 SD.

68

Approximately __% occur between the mean and ±2 SD.

95

What do you call a raw score that has been converted from one scale to another?

Standard score

What is the difference between linear and nonlinear transformation?

Linear transformation is steady and consistent in preserving the realive difference between all scores; nonlinear transformation bends the scale so its different for different scores.

Do standard scores use linear or nonlinear transformation?

Linear transformation

What do you call the atypical point that is distant from the rest of the points in the scatterplot?

Outlier

What is the mean and SD for z-scores?

Mean=0; SD=1

What is the mean and SD for t-scores?

Mean=50; SD=10

What is the mean and SD for sten?

Mean=5.5; SD=2

What is the mean and SD for stanine?

Mean=5; SD=2

What is the mean and SD for IQ?

Mean=100; SD=15

What is the mean and SD for IQ subtest?

Mean=10; SD=3

What is the mean and SD for GRE or SAT?

Mean=500; SD=100

What is the mean and SD for normal curve equivalent?

Mean=50; SD=21.06

What value must the z score be to become average?

-1,0,+1

What value must the t score be to become average?

40, 50, 60

If the value of z is -3, this indicates ; If the value of z is +3, this indicates .

Below average; above average

If the value of z is -2, this indicates ; If the value of z is +2, this indicates .

Low average; high average

If the value of t is 20, this indicates ; If the value of z is 90, this indicates .

Below average; above average

If the value of z is 30, this indicates ; If the value of z is 80, this indicates .

Low average; high average

How do you calculate the z-score?

(1) Calculate the deviation score or the difference between each score from the mean (2) Divide it by the standard deviation

How do you calculate the t-score?

(1) Multiply z-score by 10 (2) Add 50