PSYC 120 exam 1

What is the difference between sampling bias and sample error?

SAMPLE ERROR

• Differences that invariably exist between population parameters and sample statistics

• Describes the natural differences that arise from sampling (samples will never 100% represent population)

SAMPLE BIAS

what is a variable?

• characteristic or condition

• different for different individuals in a data set

What is a margin of error?

Estimated range of differences between statistic and parameter

What is the difference between discrete variables and continuous variables? Give examples.

DISCRETE VARIABLES

• Countable

• Whole numbers only

• Nothing in-between

  • Only certain numbers on an interval

    • 5 means 5

EXAMPLES = number of students in a class, number of items sold per day, number of players on a team, number of shoes in a closet

CONTINUOUS VARIABLES

• Infinite

• Decimal

• Always something in-between

  • Any value at any point along an interval

    • 5 could mean 5.1161, 5.03859, or 5.4224736

EXAMPLES = height, weight, time, temperature

What is a random sample?

each item has an equal chance of being chosen

What is the difference between a statistic and a parameter? Give examples.

statistic = used to describe a sample

parameter = used to describe a population

What is the difference between a sample and a population? Give examples.

sample = subset of a population that represents it

population = general group you’re studying about

Why can’t you randomly select individuals from a population?

selection bias

self-reporting —> selection bias

What is the difference between descriptive and inferential statistics? Give examples of each.

DESCRIPTIVE STATISTICS

Summarize, organize, and simplify data about a sample

INFERENITAL STATISTICS

Give us generalizable information about a population (bc we often have to estimate and infer from smaller sample information to population information)

What are the different types of study methods?

• Descriptive

• Correlational

• Comparative

  • Experimental

  • Nonexperimental

    • Pre-Post Study

What is the difference between an extraneous variable and a confounding variable?

EXTRANEOUS VARIABLE

• Any variable that you're not investigating that can potentially affect the DV of your research study

• Shouldn’t differ significantly between groups

EXAMPLE = participant characteristics (ie. gender, age, race, class) and environmental factors (ie. time of day, location, lighting)

CONFOUNDING VARIABLE

• A type of extraneous variable that not only affects the DV, but is also related to the IV

EXAMPLE =

what is a construct?

a variable that cannot be directly observed

EXAMPLES = childhood, gender, nationality, loneliness

When examining the relationship between two variables, what are two reasons why there may be a difference? How do you determine whether or not this difference is significant?

1) There is a real difference between group scores that is attributable to the differences in group conditions

2) The difference is due to chance (idiosyncratic fluctuations in scores) and just an artifact of sampling error

Inferential statistics

What are three ways to ensure that participant characteristics don’t differ (control other variables)?

• Random assignment

  • Each participant has an equal chance of being assigned to each of the treatment conditions

  • Distributes the participant characteristics evenly between the two groups so that neither group is noticeably more [insert characteristic] than the other

• Matching characteristics in different groups

  • Ensures groups are equivalent in terms of participant variables and environmental variables

  • Accounts for any preexisting differences between participants

    • EXAMPLE = researcher could match groups by ensuring that each group has exactly 60% females and 40% males

• Holding constants

  • EXAMPLE = The researcher in (Polman et al., 2008) used only 10-year-old boys as participants (holding age and gender constant).

The experimental method has what two characteristics that differentiate experiments from other types of research studies?

MANIPULATION

• One variable (IV) must be manipulated to create treatment conditions

• Another variable (DV) must be measured/observed to obtain scores for each condition and determine a cause-and-effect relationship

CONTROL

• Extraneous variables (participant and environmental) must be controlled so they don’t affect the relationship being studied

What statistical tests are used in a correlational study?

• Numerical = correlations

• Categorical = chi-square

What is a pre-post study?

What is a nonexperimental study?

• Examine relationships between variables by comparing groups of scores, BUT they do not have the rigor of true experiments and cannot produce cause-and-effect explanations

• Uses a preexisting participant characteristic (such as older/younger) or the passage of time (before/after) to create the groups being compared

• Can be within participants (pre-post study) or between participants (that naturally exist/nonequivalent groups

• Measure variables as they naturally occur without any further manipulation

What is a quasi-experimental study?

What are the different types of non-experimental study methods?

• Descriptive/Qualitative

  • Observational

  • Case Study

  • Survey

• Correlational

• Cross-sectional

In what scenario(s) would you be unable to conduct an experiment?

1) Unethical methodology

2) Unable reliably and feasibly measure variable

What are scores? What symbol(s) represent(s) them?

• Values that result from variable measurement

• Represented by X or Y

What is a frequency distribution? What does it include?

• Ways to organize and summarize scores in a data set

• A summary that is organized by the number of scores at each value

• Includes

  • Set of categories from the original scale of measurement

  • Frequency (number) of individuals in/with each category/score

What is proportion (p)? State the equation.

• The fraction of the total group that is associated with each score

• p = f/N

  • score frequency divided by total number of scores

• Typically expressed as a percentage

What is the difference between a percentile rank and a percentile? How are they similar?

• Both are used to describe the position of individual scores within a distribution

  • Percentile = refers to score

  • Percentile rank = refers to a percentage (of scores at or below a certain score)

EXAMPLE

You score a 1450 on the SAT, and you know that exactly 97% all test takers had scores of either 1450 or lower.

• Percentile = 97th percentile

• Percentile rank = 97%

What is a percentile rank?

• The percentage of individuals with scores AT or BELOW the particular value in a distribution

• AKA cumulative percentage (c%)

• Gives the cumulative percentage associated with a particular score

lower limit

The LOWEST something can be if it’ll be rounded UP to the normal value

EXAMPLE = 5 ft and 6 inches

• Lower limit = 5 feet and 5.50 inches

upper limit

The HIGHEST something can be if it’ll be rounded DOWN to the normal value

EXAMPLE = 5 ft and 6 inches

• Lower limit = 5 feet and 6.49 inches

What are bar graphs used for?

non-continuous data (ie. nominal or numerical but discrete variables)

What are six common things in a frequency distribution table?

• Scores (X)

• Frequency (f)

• Proportion (p)

• Percentage (%)

• Cumulative frequency (cf)

• Cumulative percentage (c%)

What is the cumulative frequency (cf)?

• Refers to the NUMBER of elements at or below a score in a distribution

• Can be used to calculated the cumulative percentage (c%) or percentile rank

What is a skewed distribution? What are the two types? Give examples.

• The scores tend to pule up toward one end of the scale and taper off gradually at the other end

• Tail points in the direction of the skew

• Positively skewed = more negative scores

  • EXAMPLE = hard exam —> more low scores —> positively skewed

• Negatively skewed = more positive scores

  • EXAMPLE = easy exam —> more high scores —> negatively skewed

What types of graph(s) are/is used for nominal or ordinal data?

Bar graphs

What types of graphs are used for population distribution?

The following are used when presented with large amounts of data:

• Relative frequency graph

  • X-axis = category

  • Y-axis = percent

• Smooth curves

  • X-axis = scores

  • Y-axis = frequency

What are three characteristics that can thoroughly describe any frequency distribution?

• shape (symmetrical or skewed)

  • smooth curves

• central tendency (mean/median/mode)

  • representative statistic (where center or distribution is located) → usually the average

• variability (variation/SD)

  • extent of spread/clustering of data

What is a symmetrical distribution?

How do you graph continuous and discrete variables on a histogram?

CONTINUOUS

• bars are touching

• bar width corresponds to real limits of variable for continuous variables

DISCRETE

• bars are separate

When are smooth curves used? What do they show? Explain axes.

• When there’s ALOT of data

• Used to indicate exact scores weren’t used

• Shows where scores generally fall in a population

• Axes

  • X = scores (X)

  • Y = frequencies (f)

Polygon

• A dot appears where the center of the top of each bar would be in a histogram

  • corresponds to the frequency for the category

• A continuous line is drawn from dot to dot to connect the series of dots

• The graph is completed by drawing a line down to the X-axis (zero frequency) at each end of the range of scores. The final lines are usually drawn so that they reach the X-axis at a point that is one category below the lowest score on the left side and one category above the highest score on the right side.

What types of graphs can be used for interval or ratio data?

• histograms

• informal histograms

• polygons

What is a stem and leaf plot?

• A simple alternative to a grouped frequency distribution table or graph

• Each score is separated into two parts: a stem and a leaf

  • Stem = First digit (or digits)

  • Leaf = Last digit

• EXAMPLE = If X = 85 → stem = 8 and leaf = 5 ●

• Gives us similar information to graphs at first glance

• Every individual score can be identified

• Also gives us information about each score in the data set

A data set has the following statistics:

• mean = 89

• median = 66

• mode = 43

Is the distribution of this data set symmetrical or skewed? If skewed, is it a positive or negative skewed?

positively skewed

A data set has the following statistics:

• mean = 29

• median = 32

• mode = 41

Is the distribution of this data set symmetrical or skewed? If skewed, is it a positive or negative skewed?

negatively skewed

What is the purpose of central tendency? What are the three measures of central tendency?

• To determine the single value that identifies the center of the distribution and best represents the entire set of scores

• Mean, median, mode

What may be two reasonings that may explain a difference between two groups?

1) Error

2) Significant Difference

What is a nominal scale? Give examples.

• Consists of categories that differ only in NAME and are not differentiated in terms of magnitude or direction

• Label and categorize

• No quantitative distinctions

  • Numbers have no ‘real meaning’ other than differentiating between object

EXAMPLES

• GENDER: Females = 1, Males = 2

• UNIFORM NUMBERS: The numbers on the uniforms differentiate the different players and doesn’t provide insight on what position they’re in or how skilled they are

• Others: diagnosis, experimental or control

What is an ordinal scale? Give examples.

• The categories are differentiated in terms of direction, forming an ordered series

  • Categorizes observations

  • Categories are organized by size or magnitude

• Assigns numbers to categories, but there is a meaningful order (indicates placement)

• Doesn’t indicate differences in magnitude

EXAMPLES

• Rank in class (1st, 2nd, 3rd)

• Level of satisfaction (ie. survey)

• Placement in an Election (1st, 2nd, 3rd)

• Clothing sizes (S, M, L, XL)

• Olympic medals (gold, silver, bronze)

What is an interval scale?

• Consists of an ordered series of categories that are all equal-sized intervals

  • Possible to differentiate name, direction and distance (magnitude differences) between categories

    • Labeled categories (have names)

    • Ordered categories (numbers have order)

    • Interval between categories of equal size

• Arbitrary or absent zero point → ratios are not meaningful

EXAMPLES

• Temperature = difference between 79°C and 80°C is the same as that between 40°C and 41°C

  • 80°C is higher than 79°C and 41°C is higher than 40°C

  • No zero point → 0°C has a “value” → ratios are NOT meaningful

    • 80°C is NOT twice as hot as 40°C

• IQ = difference between 100 and 110 is the same as that between 140 and 150

  • 110 is higher than 100 and 150 is higher than 140

What is a ratio scale?

• An interval scale for which the zero point indicates none of the variable being measured

• Labeled categories (differentiated by name)

• Ordered categories

  • Order has meaning

• Equal interval between categories

  • Magnitude differences are meaningful

• Absolute/true zero point → ratios are meaningful

EXAMPLES

• Number of correct answers

• Time to complete task

• Height

• Weight

What additional information is obtained from measurements on an ordinal scale compared to measurements on a nominal scale?

• Direction of difference (greater or less) between two measurements (order has meaning)

  • You know the placement/position of each category relative to the others

• EXAMPLE = runners in a race

  • 1st place > 2nd place > 3rd place (ie. time)

• EXAMPLE = ranking movie satisfaction on a scale from 1-5

  • 1 = that shi sucks ass booty cheeks; im burning down any movie theaters that show it

  • 5 = im giving the director/producer head fr

What additional information is obtained from measurements on an interval scale compared to measurements on a ordinal scale?

• Magnitude of Difference b/w two measurements

  • You can know the numerical difference between each category b/c intervals are equal

  • No true zero → can only add/subtract values

  • Answers: “this movie got more votes/is more popular than the other (ordinal), but by how much?”

• EXAMPLE = how hot you are (temperature)

  • Bill Nye is hotter than Michael B. Jordan by 400,000°C and hotter than Henry Cavil by 420,000°C

    • Bill Nye = 500,000°C (GYATT)

    • Michael B. Jordan = 100,000°C

    • Henry Cavil = 80,000°C

  • Nominal → names (bill, michael, henry)

  • Ordinal → bill > michael > henry

What additional information is obtained from measurements on an ratio scale compared to measurements on a interval scale?

• True/Absolute Zero Point → can calculate ratios

  • The ratio of two measurements, which allow comparisons such as “twice as much.”

• EXAMPLE = how many people you can pull in a semester

  • Out of all three people (Jack, Ronald, Colin), Ronald pulled 3x more people than Jack

    • Ronald = pulled 12 people (mostly because his name is so so hot) in a semester

    • Jack = pulled 4 bitchez

    • Colin = get ZERO bitchez this semester

  • Nominal → names (jack, ronald, colin)

  • Ordinal → ronald > jack > colin

  • Interval → ronald pulled 8 more ppl than jack and 12 ppl more than colin

Describe the data for a correlational research study and explain how these data are different from the data obtained in experimental and nonexperimental studies, which also evaluate relationships between two variables.

• A correlational study has only one group of individuals and measures two (or more) different variables for each individual.

• Other research methods evaluating relationships between variables compare two (or more) different groups of scores.

The results of a recent study showed that children who routinely drank reduced fat milk (1% or skim) were more likely to be overweight or obese at ages 2 and 4 compared to children who drank whole or 2% milk (Scharf, Demmer, & DeBoer, 2013).

a. Is this an example of an experimental or a nonexperimental study?

b. Explain how individual differences could provide an alternative explanation for the difference in weight between the groups.

c. Create a research study that would be able to differentiate among those interpretations of the results.

A

• Nonexperimental

  • No IV is manipulated

  • Participants are not randomly assigned to groups that receive different amounts of milkfat

B

• Individual differences (ie. characteristics, environmental factors) can impact DV (ie. lifestyle, genetics, and home life)

  • EXAMPLE = participants in the reduced milkfat (skim or 1% milk) group (regularly drank reduced-fat milk) also tended to be more sedentary

C

• 1 = A researcher could randomly assign participants to groups that receive different amounts of milkfat

• 2 = A researcher could assign participants to two groups that receive different amounts of milkfat

  • Holding constant characteristics (ie. amount of physical activity by participants in each group)

• 3 = A researcher could assign participants to two groups that receive different amounts of milkfat

  • Matching the two groups in the amount of physical activity

A tax form asks people to identify their age, annual income, number of dependents, and social security number.

For each of these four variables, identify the scale of measurement that probably is used and identify whether the variable is continuous or discrete.

• Age: ratio scale and continuous

  • Although people usually report whole-number years, the variable is the amount of time and time is infinitely divisible

• Income: ratio scale and discrete

  • Income is determined by units of currency. For U.S. dollars, the smallest unit is the penny and there are no intermediate values between 1 cent and 2 cents.

• Dependents: ratio scale and discrete

  • Family size consists of whole-number categories with no intermediate values.

• Social Security: nominal scale and discrete

  • Social security numbers are essentially names that are coded as 9-digit numbers. There are no intermediate values between two consecutive social security numbers.

Ackerman and Goldsmith (2011) compared learning performance for students who studied material printed on paper versus students who studied the same material presented on a computer screen. All students were then given a test on the material and the researchers recorded the number of correct answers.

a. Identify the dependent variable for this study.

b. Is the dependent variable discrete or continuous?

c. What scale of measurement (nominal, ordinal, interval, or ratio) is used to measure the dependent variable?

a. Number of correct answers on the test (a measure of knowledge of the material)

b. Knowledge is a continuous variable. If it is measured with a 10-question test, it may appear to be discrete but it could be measured with a 100-question test, which means that each category can be further divided.

c. Ratio scale (has absolute zero = complete absence of correct answers)

Doebel and Munakata (2018) discovered that delay of gratification by children is influenced by social context. All children were told that they were in the “green group” and were placed in a room with a single marshmallow. Participants were told that they could either eat the single marshmallow now or wait for the experimenter to return with two marshmallows. Before choosing between one marshmallow now or two later, children were randomly assigned to one of two conditions. They were told that either (1) other children in the green group waited and kids in the orange group didn’t wait or (2) other children in the green group didn’t wait and kids in the orange group waited. Children were more likely to choose to wait after being told that other members of their group waited.

a. Did this study use experimental or nonexperimental methods? b. Identify the variables in this study

A

Experimental method = participants were randomly assigned to groups that received different instructions

B

IV = instructions received by participants (being told that their group waited and the other didn’t vs. being told that their group didn’t wait and the other group waited)

DV = behavior (whether or not children chose to wait for a larger reward)

How does the median and mean differ in terms of their “middle” definition?

median = 50% percentile (by score)

mean = midpoint (by distance)

multimodal distribution

multiple modes

bimodal distribution

two modes

trimodal distribution

three modes

How do you calculate weighted mean?

(total sum of scores from both data sets) divided by (total items from both data sets)

What happens to the mean when changing (increasing/decreasing) a score in a data set?

↑ score =↑ mean

↓ score = ↓ mean

What happens to the mean when adding or removing a score (larger than, equal to, and smaller than the mean) to/from the data set?

ADDING OF A SCORE

• Adding a score LARGER THAN mean = ↑ mean

• Adding a score EQUAL TO mean = no change

• Adding a score SMALLER THAN mean = ↓ mean

REMOVING A SCORE

• Adding a score LARGER THAN mean = ↓ mean

• Adding a score EQUAL TO mean = no change

• Adding a score SMALLER THAN mean = ↑ mean

Besides being the sum of the scores divided by the number of scores (arithmetic average), what are two alternative definitions of a mean?

• Dividing the Total Equally = the amount each individual receives when the total is distributed equally

• Balance Point = total distance below the mean is the same as (balanced by) the total distance above the mean

  • Regardless of the distribution, a seesaw would be balanced at the mean

What happens to the mean when adding or subtracting a constant from each score?

• The score changes (increases/decreases) by the same amount you change it by

  • Adding 5 to each score changes the mean by +5

    • M = 20 → 25

  • Subtracting 5 to each score changes the mean by -5

    • M = 20 → 15

What happens to the mean when multiplying or dividing a constant from each score?

• The score changes (increases/decreases) by the same factor

  • Multiplying 5 to each score changes the mean by x5

    • M = 20 → 100

  • Dividing 5 to each score changes the mean by x1/5

    • M = 20 → 4

What is a skewed distribution?

• A strong tendency for the mean, median, and mode to be located in predictably different positions

  • Mode = located toward the side where the scores pile up

  • Mean = pulled toward the extreme scores in the

• Negatively skewed or positively skewed

What does it mean if a distribution is positively skewed?

mode < median < mean

mean is the greatest value

What does it mean if a distribution is negatively skewed?

mean < median < mode

mean is the smallest value

Define the mean, median, and mode.

mean = balance point of distribution; midpoint of the dataset (by distance)

median = midpoint of the dataset or distribution (by score)

mode = score with the highest frequency

Define the mean

TRUE OR FALSE: The mode is a frequency.

FALSE: The mode is the category with the largest frequency

When do you use the mode to describe a data set (over a mean)?

• Nominal Scales

• Discrete Variables

• Describing Shape

When would you use the median to describe a data set (over a mean)?

• Extreme Scores or Skewed Distributions

  • Unlike the mean, it isn’t easily influenced by outliers

• Undetermined (infinite) Values

  • Impossible to calculate mean if there are infinite values

• Open-Ended Distributions

• Ordinal Scale

Why is the mean typically considered the best and most commonly used central tendency? What is it useful for?

• Takes every score/value in the distribution/dataset into account

• Closely related to variance and standard deviation

  • Useful for inferential statistics

One sample of n=4 scores has a mean of M=10, and the second sample of n=0 has a mean of M=0. If the two samples are combined, then what value will be obtained for the mean of the combined sample?

a) equal to 15

b) greater than 15 but less than 20

c) less than 15 but more than 10

d) none of the above.

c) less than 15 but more than 10

The overall weight will be more weighted towards the data set with more

Find the precise median for the following scores measuring a continuous variable.

Scores: 1 4 5 5 5 6 7 8

a) 5

b) 5.17

c) 5.67

d) 6

b) 5.17

While the discrete median would be 5 (whole #) the continuous median could be any value between 5.00 and 5.49 (any decimal that would round to 5.00)

A population of N=10 scores has a mean of 30. If every score in the distribution is multiplied by 3, then what is the value of the new mean?

a) still 30

b) 33

c) 60

d) 90

d) 90

Multiplying or dividing each score will change the mean by the same factor.

A population of scores has a mean of = 100. Calculate the mean for each of the following:

a. A constant value of 50 is added to each score

b. A constant value of 50 is subtracted from each score

c. Each score is multiplied by a constant value of 2

d. Each score is divided by a constant value of 50.

a) 150

b) 50

c) 50

d) 2

A sample of n=6 scores has a mean of M=10. If one score was changed from X=21 to X=10, what is the value of the new sample mean?

6

If the mean, median, and mode are all computed for a distribution of scores, which of the following statements cannot be true?

a) No one had a score qual to the mean

b) No one had a score equal to the median.

c) No one had a score equal to the mode.

d) None of the above.

c) No one had a score equal to the mode.

???

A sample of n=6 scores has a mean of M=10. If one score with a value of X=12 is removed from the sample, then what is the value of the new sample mean?

9.60

A sample has a mean of M=72. If one person with a score of X=98 is removed from the sample, what effect will it have on the sample mean?

a. The sample mean will increase.

b. The sample mean will decrease.

c. The sample mean will remain the same.

d. Cannot be determined from the information given.

b. The sample mean will decrease.

For a distribution of scores, the mean is equal to the median. What is the most likely shape of this distribution?

a. Symmetrical

b. Positively skewed

c. Negatively skewed

d. Impossible to determine the shape

a. Symmetrical

For a positively skewed distribution with a mode of X=20 and a median of X=25, what is the most likely value for the mean?

a. Greater than 25

b. Less than 20

c. Between 20 and 25

d. Cannot be determined from the information given

a. Greater than 25

For a positively skewed distribution, the mean is GREATER THAN the median, which is greater than the mode (mean>median>mode). Therefore, the mean has to be GREATER THAN both 20 and 25.

For a negatively skewed distribution with a mode of X=37 and a median of X=28, what is the most likely value for the mean?

a. Greater than 37

b. Less than 28

c. Between 28 and 37

d. Cannot be determined from the information given

b. Less than 28

For a negatively skewed distribution, the mean is LESS THAN the median, which is less than the mode (mean<median<mode). Therefore, the mean has to be LESS THAN both 37 and 28.

For a positively skewed distribution, what is the most probable order for the three measures of central tendency from smallest to largest?

a. Mean, median, mode

b. Mean, mode, median

c. Mode, mean, median

d. Mode, median, mean

d. Mode, median, mean

For a positively skewed distribution, the mean is GREATER THAN the median, which is greater than the mode (mean>median>mode).

Therefore, from smallest to largest, it is mode<median<mean.

A researcher is measuring problem-solving times for a sample of n=20 laboratory rats. However, one of the rats fails to solve the problem so the researcher has an undetermined score. What is the best measure of central tendency for these data?

a. The mean

b. The median

c. The mode

d. Central tendency cannot be determined for these data.

b. The median

The median would be chosen over the mean as a central tendency in the following scenarios: (1) Extreme Scores or Skewed Distributions, (2) Undetermined Values, (3) Open-Ended Distributions, and (4) Ordinal Scale.

What is the best measure of central tendency for an extremely skewed distribution of scores?

a. The mean

b. The median

c. The mode

d. Central tendency cannot be determined for a skewed distribution.

b. The median

The median would be chosen over the mean as a central tendency in the following scenarios: (1) Extreme Scores or Skewed Distributions, (2) Undetermined Values, (3) Open-Ended Distributions, and (4) Ordinal Scale.

One item on a questionnaire asks students to identify their preferred animal for the school mascot from three different choices. What is the best measure of central tendency for the data from this question?

a. The mean

b. The median

c. The mode

d. Central tendency cannot be determined for these data.

c. The mode

The median would be chosen over the mean as a central tendency in the following scenarios: (1) Nominal Scale, (2) Discrete Values, and (3) Describing shape.

What is variability?

• The degree to which scores are clustered or spread out

• How peaked the curve is

• How similar data points are to one another

  • Consistency or diversity

• Distance between scores

• Distance between a score and the mean

• Affects how well any single score could represent the whole

What are the four basic ways of measuring variability?

• Range

• Interquartile range

• Standard deviation

• Variance

What is range?

• Distance covered by the set of scores (between smallest and largest score)

• When upper and lower boundaries are precise

• Xmax- Xmin 

What are some drawbacks for using range for measuring variability?

• Very sensitive to outliers

• Reflects information about extreme values but not much about the middle values

What is interquartile range (IQR)? How is it calculated?

• The scores that make up the middle 50% of a range (25% to 75% or 1st quartile to 3rd quartile)

  • Imagine dividing combined scores into 100 equal parts

    • Each of these represents 1% of the data

  • quartile = score at each 25% interval

• Q3 - Q1 = IQR

Why is IQR a better description of variability in data than range?

It trims the extreme scores and provides a range that reflects the middle 50% of scores in the center of the distribution

What is deviation?

What is standard deviation? What symbols represent it?

• The square root of the variance

• Provides a measure of the standard distance from the mean

What is variance? What symbols represent it?

the mean squared deviation (mean of sum of squares)