PY 211 Test 1

When to use which measure of central tendency: Mode

-In a modal shape distribution (prominent mode such as unimodal or bimodal distributions) -In a nominal measurement scale

When to use which measure of central tendency: Mean

-In a normally shaped distribution -In an interval or ratio scale of measurement

Two branches of statistics

1. Descriptive: Summarizes, organizes, and describes scores. -Putting numbers into pie charts for college of Arts & Sciences majors 2. Inferential: Allows sample results to be generalized to representative populations. -Polling data: sample of people polled and asked who they voted for -> Based on the sample, what we think the outcome of the election will be! -We cannot generally gather data from everyone. -Like all UA students (38k), we might use a sample of 1k UA students instead.

Population vs. Sample

1. Population: Entire set of individuals or items of interest. -Data are termed PARAMETERS. -All UA students -> % who engage in COVID risk behaviors, cannot get to all 30k+ students, but what if we poll a statistics class of 76? Is it representative? A 211 class is typically composed of sophomore, what do seniors think? 2. Sample: Representative subset of a population. -The stats class of 76. -Data are termed STATISTICS. -Most behavioral research is done on samples. -Descriptive stats SUMMARIZE sample results. -Inferential stats GENERALIZE to populations.

Quantitative vs. Qualitative Data

1. Quantitative: Varies by amount. -Example: Age by number of years alive. 2. Qualitative: Varies by form or class. -Example: Gender, race, ethnicity, religion, low or high SES. -Affects the type of data analyses possible.

A. CONTINUOUS OR DISCRETE B. QUALITATIVE OR QUANTITATIVE C. SCALE OF MEASUREMENT USED Duration of drug abuse (in years)

a. Continuous b. Quantitative c. Ratio

A. CONTINUOUS OR DISCRETE B. QUALITATIVE OR QUANTITATIVE C. SCALE OF MEASUREMENT USED The size of a reward (in grams)

a. Continuous b. Quantitative c. Ratio

A. CONTINUOUS OR DISCRETE B. QUALITATIVE OR QUANTITATIVE C. SCALE OF MEASUREMENT USED Number of errors

a. Discrete b. Quantitative c. Ratio

A. CONTINUOUS OR DISCRETE B. QUALITATIVE OR QUANTITATIVE C. SCALE OF MEASUREMENT USED Number of lever presses per minute

a. Discrete b. Quantitative c. Ratio

Approximately rectangular frequency distribution

-After a histogram, researchers draw a curve/line over the the touching bars to understand the shape of that frequency distribution. -Not a lot of difference/variance in our data (between each score). Most scores occur at close to the same frequency.

Approximately bimodal frequency distribution

-After a histogram, researchers draw a curve/line over the the touching bars to understand the shape of that frequency distribution. -Two overall points that occur the most frequently.

Unimodal frequency distribution

-After a histogram, researchers draw a curve/line over the the touching bars to understand the shape of that frequency distribution. -UNIMODAL: 1 score that has the highest frequency (the mode: the score that is occurring the most frequently.)

Central Tendency

-The most typical or common score. -3 methods to finding central tendency: mode, median, mean.

Ordinal Scale of Measurement

2. Ordinal/Rank-Order: Rank or order. Can be ordered BUT there is a variety of differences between these rankings, not equal distanced. -Example: Class rankings first through last. You could be 1st in class with a 4.33 GPA whereas 2nd could be 4.23, BUT 3rd in class could have a GPA of 3.98. -NOT EQUAL DISTANCED!

Ratio Scale of Measurement

4. Ratio/Ratio-Scale: Has an order with equal units AND an absolute zero. -Example: Height in inches. If something does not exist, there is no height, so h=0.

A. CONTINUOUS OR DISCRETE B. QUALITATIVE OR QUANTITATIVE C. SCALE OF MEASUREMENT USED Number of students in your class

a. Discrete b. Quantitative c. Ratio

Simple frequency distribution -The use of frequency tables

-A summary display for: a. The frequency of scores falling within defined groups or intervals (grouped data) in a distribution. OR b. The frequency of each individual score or category (ungrouped data) in a distribution. ____________________________________________________________________ -A frequency table describes the data, makes the pattern of the data clear, and shows how many scores there are for each value on the scale.

Ungrouped Data in a frequency table -Why are some scores/categories ungrouped?

-Assess a group of data. -Find the lowest and highest value. -Put all possible values to the far left column (example: all possible stress ratings from 0-10). -Then count how many of each value was given. Put that in the Frequency Column. -Then conduct a % -> frequency of score / total number of scores. -Ungrouped Data: a set of scores or categories distributed individually, where the frequency for each individual score or category is counted. -Typically data are ungrouped when the number of different scores is small and for categorical variables (gender, religion, race). -You could see white/nonwhite grouped, but you lose the nuance of the information. Unable to see the diversity of individual races in the nonwhite category. Same happens with religion.

Scales of Measurement

-Coined by S.S. Stevens, a Harvard psychologist -Degree to which measured variables conform to the abstract number system. Age can be put into a number system much like how new parents count the number of months their child is alive. -Includes: identity (categories), order (can they be ordered?), equal distance (is there equal distance between each value in that sequence), and absolute zero (i.e. can there be a complete absence of that variable?) -This system of identity/order/equal distance/absolute zero determines the type of statistical analyses possible. -Like a decision tree; determined by the type of variable you are using. The types of scale indicate what the number represents. 1. Nominal: Identity or classification ONLY. -Example: 1 = Men, 2 = Women, 3 = Non-Binary -Can also be race, ethnicity, and religion. 2. Ordinal: Rank or order. Can be ordered BUT there is a variety of differences between these rankings, not equal distanced. -Example: Class rankings first through last. You could be 1st in class with a 4.33 GPA whereas 2nd could be 4.23, BUT 3rd in class could have a GPA of 3.98. -NOT EQUAL DISTANCED! 3. Interval: Order and equal units. -Example: Achievement test scores (SAT, ACT). -Equal distanced but there is no absolute zero (there is no absence of the variable). -You can put the values in an order and the differences are equal. EXAMPLE: The difference between 1 and 2 would be the same as the difference between 2 and 3. 4. Ratio: Has an order with equal units AND an absolute zero. -Example: Height in inches. If something does not exist, there is no height, so h=0.

IQ Score Importance

-Data like the previous examples can be used to categorize people. -A diagnosis of an intellectual disability requires an IQ score of 70 or below. Based on the typical SD=15, M=100. -Being put in gifted or higher-level classes. -CAN HAVE LIFE OR DEATH CONSEQUENCES: -A lot of states who still have the death penalty use a federal ruling of Adkins v. VA from 2002. You cannot sentence someone to death if they are diagnosed with an intellectual disability (they may not know the true effects of their actions on others). -However, if someone takes multiple IQ scores and if even one of them has an IQ score above 70, like a 72, they could be tried for death. Brettline Rules.

Scattergram

-Displays discrete data points (x, y) to summarize the relationship between two variables. -Data points are plotted to see whether a pattern emerges. -Photo example: High high school GPAs correspond to high first year GPAs.

Standard Deviations and Normal Distributions

-For normal distributions, with any mean and any variance, we can make the following three statements: 1. At least 68% of all scores lie within 1 SD of the mean. 2. At least 95% of all scores lie within 2 SD of the mean. 3. At least 99.7% of all scores lie within 3 SD of the mean. -Example: M=4, SD=1.8 68% of our data should be between the raw scores of 2.2 and 5.8.

Measures of Central Tendency: Normal skew, positive skew, negative skew

-In a normal distribution: the mean/median/mode coincide (all equal to each other or are close to the same place). -In skewed distributions, the mean is PULLED toward the TAIL of the distribution. -Positively skewed distribution: The mean is greater than the median (right tail, skew right, mean right). -Negatively skewed distribution: The mean is less than the median (left tail, skew left, mean left).

When to use which measure of central tendency: Median

-In a skew shaped distribution (with outliers in the direction of the skew) -In an ordinal measurement scale

Recap of Information: raw scores, the mean of raw scores, the standard deviation of raw scores from the mean

-Knowing one score tells little about how it relates to the whole distribution of scores. (X=5). -Comparing a score to the mean of a distribution does indicate whether a score is above or below average (X=5, M=4). If the mean of exam scores is 83 and someone got a 77, you would know that score is below average, whereas someone with an exam score of 95 would have a score above average. -Knowing the standard deviation of a distribution indicates how much above or below average a score is in relation to the spread of scores in the distribution. (X=5, M=4, SD=1).

The Tyranny of the Mean & The Mean and SD used in research articles

-Knowledge about the individual case is lost when taking averages. -Sometimes we use qualitative research methods like case studies or ethnographies to get a deeper understanding of what is happening in an individual case. -Example: Focus groups, interviewing people, understanding more about their experiences. -Example: If an individual's number of hours of sleep every night is just couched within everyone else, then the person who gets 3 hours a night, the information about what might be happening for them or what might be a barrier for them to get more sleep is lost in just saying, "People on average sleep between 6 and 9 hours each night." -If possible, use BOTH quant. and qual. data. ________________________________________________________________________ -The mean and SD are commonly reported in research articles such as this article for stress resilience in marriage. On 4 scales

Mode

-Most frequently occurring number in a distribution. -Usually the measure of central tendency for nominal variables (category-based information like gender, orientation, race/ethnicity, cannot take an average of someone's race). -Example: Number of dreams during a week for 10 students. 7, 8, 8, 7, 3, 1, 6, 9, 3, 8. The mode is the HIGH POINT in the distribution's histogram. Or in this case bar chart with nominal variables.

Grouped Data in a frequency table

-Same process except you GROUP possible values equally into intervals. -Grouped Data: Set of scores distributed into intervals, where the frequency of each score can fall into any one interval. -Interval: Discrete range of values within which the frequency of a subset of scores is contained. -Make sure your intervals are the same size! -DO NOT DO THIS: 90-99, 80-89, 70-79, 60-69, 56-59, 50-55

The Normal Curve Table

-Shows the precise percentage of scores between the mean (Z-score of 0) and any other Z-score. -Table also includes the precise percentage of scores in the tail of the distribution for any Z-score. -Table lists positive z-scores, but you can flip the sign if you have a negative z-score and the side of the normal curve you work on.

Histograms

-Summarizes the frequency of continuous data that are grouped. 1. Vertical rectangle represents each interval, and height of the rectangle equals the frequency recorded for each interval. 2. Base of each rectangle begins and ends at the upper and lower boundaries of each interval. -Example: 0-2.5 months, 2.5 months-5 months. The next interval starts where the previous one left off and goes the same amount of distance. 3. Each rectangle touches adjacent at the boundaries of each interval. DATA THAT WILL NOT BE DISCRETE LIKE A CATEGORY, BUT DATA THAT CAN RANGE.

Bar Chart

-Summarizes the frequency of data in whole units or categories. -Discrete and categorical data (gender, race, religion, orientation)! -NOMINAL DATA. - Also DISCRETE DATA. Example: Number of naps per day. -Each category is represented by a rectangle. -Each rectangle does not touch along the x-axis as opposed to a histogram.

Pie Chart

-Summarizes the relative percent of discrete and categorical data into sectors. -Sector: represents the relative percent of a particular category. -Photo example: -The relative percent of the whole pie is 100%. -The RP of high school or less is about 60%. -Associates is about 15%.

The Normal Distribution/Curve and the percentage of areas under the normal distribution

-Symmetrical, unimodal (one peak only), most scores fall near the center with fewer at the extremes. -Normal curve and percentage of scores between the mean and 1 and 2 and 3 standard deviations from the mean. -Example between Mean (0) and +1 or -1 SD from the mean is 34%. -Between 1 and 2 (positive or negative) is 14%. -Between 2 and 3 (positive or negative) is 2%. -Between -3 and 0 or +3 and 0 is 50%.

Probability

-The expected relative frequency of a particular outcome. -Outcome: Result of an experiment or any life event P = possible successful outcomes / all possible outcomes -Example: Probability of getting a number of 3 or lower on a throw of a standard die = 3/6 = p=0.5 -WRITE PROBABILITIES IN DECIMAL FORM!

Advantages of the mean

-The most stable measure of central tendency because all the scores in a distribution are included in its calculation (not true to the mode or median). -You could have outliers and your mode/median would not change, but outliers do change the mean. -Not as affected by addition or deletion of scores as the mode and median are. Both will immediately move and could move significantly if a wide spread of score (like a mode from 8 to 23). -The mean is used in many statistical procedures.

Z-scores and changing a raw score to a z-score

-The number of standard deviations a score is above or below the mean. -Raw score -> z-score: Z = X-M/SD -Example: M=10, SD=5. A score of 15 would be a z-score of 1 because that raw score is 1 SD above the average. A score of 5 is 1 SD below the average, so its z-score is -1. -Raw score above the mean = positive z -Raw score below the mean = negative z -Raw score that is the mean = z-score of 0 -Remember, the mean is what falls right in the center of the normal curve, our highest point. Our PEAK in a unimodal distribution if a normal curve. -NEGATIVES MATTER for z-scores because it tells you which side of the average a z-score/raw score is falling. -Examples: M=20, SD=5 Raw score: 30, z= (+)2 15, z= -1 20, z=0 22.5, z= (+)0.5

Measures of Variability: Standard Deviation

-The square root of the variance or the average deviation from the mean. SD = square root of SD^2 = square root of E (X-M)^2/N = square root of SS/N -This is all different ways of notating the same process. -Example: Find the SD, SS=48, N=6. 48/6 = 8, square root of 8 = 2.83. SD = 2.83. -So on average, the scores are deviating from the mean about 2.7 points. On average, 1 SD away from our mean of 5 would be + or - 2.7 points. -Example: If our SD was 1.8 and our data was 6, 1, 4, 2, 3, 4, 6, 6, you would find the M=4. So, most of the data are within 1.8 or 1.8x2 points of this mean of 4, this will encompass most of your data.

Mean

-The sum of all the scores divided by the number of scores. M = EX / N E (greek letter not the actual letter E) = add everything up. X = raw score N = number of scores -Example: Number of dreams during a week for 10 students. 7, 8, 8, 7, 3, 1, 6, 9, 3, 8 EX = 7 + 8 + 8 + 7 + 3 + 1 + 6 + 9 + 3 + 8 = 60 N = 10 Mean = 60 / 10 = 6 -Place a cylinder and it would balance itself out (same amount on either side).

Median

-The value at which 1/2 of the ordered scores fall above and 1/2 the scores fall below. -The middle score when all scores are arranged from lowest to highest. -Example: Number of dreams during a week for 10 students. 7, 8, 8, 7, 3, 1, 6, 9, 3, 8. PUT IN ORDER: 1, 3, 3, 6, 7, 7, 8, 8, 8, 9. -The median is the average (mean) of the 5th and 6th scores, so the median is 7. (7+7/2=7). Put your data in order! Odd number of scores: 1, 2, 3, 4, 5. Median would simply be 3. Even number of scores: 1, 2, 3, 4. Go right between the two most middle scores, take the average of them. 2.5. Half the scores occur below and 1/2 occur above 2.5.

The Sum of Squares (the numerator in the variance formula)

-Three reasons why we square each deviation in the numerator when computing variance: E (X-M)^2 1. The sum of the differences of scores from their mean is zero. -To avoid this, each deviation is squared to produce the smallest positive solution (standard across all numbers). 2. The sum of the squared differences of scores from their mean is minimal. -Squaring deviations provides a solution with minimal error. 3. Squaring scores can be easily corrected by taking the square root. You can reverse your data if you needed to know something else about it.

Range of probabilities and probabilities as symbols

1. As a proportion: from 0 to 1 -Example: 3/6 -> p=0.5 (between 0 and 1) 2. As a percentage: from 0% to 100% -Example: p=0.5 -> p=50% AS SYMBOLS: p (in most research areas) p < 0.5 (The result in an experiment or survey is significant because it has less than 5% or 0.05 probability of happening just by chance. There is likely something happening in this situation that is influencing the data that makes this not just a random occurrence.) -The normal distribution can be seen as a probability distribution too! -Example: The % of scores between any two z-scores is the same as the probability of selecting a score between those 2 z-scores. -Selecting a score randomly between -2 z and -1 z, there is a proportion of 0.14, or probability percentage of 14%, not a large chance. Closer to the tails you get, the rarer the occurrence.

Continuous vs. Discrete Data

1. Continuous: Divisible into an infinite number of fractional parts; POSSIBLE DECIMALS. 2. Discrete: Separate and indivisible categories; WHOLE NUMBERS ONLY. -Nominal variables. -Example: The average household has 2.5 kids. This is NOT CONTINUOUS. There cannot be 2.5 kids.

Definitional vs. Computational Formulas

1. Definitional Formulas: A usual formula that directly shows you the meaning of the procedure. -Variance: The mean squared difference between a score and the mean of all the scores. 2. Computational Formulas: Easier to figure out by hand, but it does not directly show the meaning of the procedure. -Variance: SD^2 = E (X-M)^2 / N

The Controversy of Graphs

1. Failure to use equal interval sizes. -Example: New York Times, 1978. Travel agents are not making as much commission as they used to. The first two bars the histogram show the ENTIRE YEAR whereas the last shows only the FIRST HALF OF THAT YEAR. Unequal intervals! 2. Exaggeration of proportions. -Example: 2008 recession, mean house price. Starting your histogram y-axis at $150k versus $0 makes the drop in price look much larger due to the much smaller scale. -Example: How people squash data by using different dimensions despite the same data. Making your histogram look shorter and wider versus longer and taller.

Frequency and frequency distribution

1. Frequency: describes the number of times or how often a category, score, or range of scores occurs. -Example: Ask the class' age. Frequency of how many students are 18, 19, 20, 21, etc. If 5 people claim they are 20, the value 20 would have a frequency of 5. 2. Frequency Distribution: A summary display for a distribution of data.

Nominal Scale of Measurement

1. Nominal: Identity or classification ONLY. -Example: 1 = Men, 2 = Women, 3 = Non-Binary -Can also be race, ethnicity, and religion.

More on Samples and Populations and Methods of Sampling

1. Population: ALL Canadian women for example. You can very rarely survey or get data from an entire population, like every single UA student. 2. Sample: Getting large enough samples so it is representative of what is happening in a population at that moment. 50 Canadian women for example. How a candidate is polling - sample of 1,000 voters out of a population of all voters. Methods of Sampling: 1. Random Selection: The gold star, what researchers aim for. Sampling using truly random procedures - each person has an equal chance of being selected. -Example: Research to begin with a complete list of all the people in that population and selecting a group of them to study by a table of random numbers. -It can be hard to get a random selection due to a lot of things: selection biases (someone might be more interested in a topic or subject matter of a survey and so they might select into that particular sample) -Example: Polling data, getting a random selection of all voters and you do it through phone, when not everyone had a phone back then. You may only be sampling those in a higher SES or income. 2. Haphazard Selection: Taking whoever is available or whoever happens to be first on a list; this is why you do not alphabetize a list and select the first few. -It is easy to accidentally pick up a group very different from the population as a whole. -Example: Just surveying from friends and coming to a conclusion.

Properties of Z-scores

1. The sum of a set of z-scores is always zero because the mean has been subtracted from each score, and following the definition of the mean as a balancing point, the sum and average of deviation scores must be zero. (X - M) / SD 2. The SD of a set of standardized scores is always 1 because the deviation scores have been divided by the SD. Dividing the SD in those formulas standardizes the data so that the SD then of the z-score is always 1. (X - M) / SD

Variable, Value, Score

1. Variable: A category/characteristic that can have different values. -Examples: Stress level, age, gender, religion, engagement in COVID-risk behaviors. 2. Value: ALL POSSIBLE ANSWERS IN A CATEGORY, a possible number or category that a score can have. -Examples: 0-4, 18-100, Woman/Man/NB/Trans, Muslim/Hindu/Sikh/Catholic/Agnostic, Yes/No 3. Score: A PARTICULAR ANSWER IN A CATEGORY BY AN INDIVIDUAL, a particular person's value on a variable -Examples: 0/1/2/3/4, 25/85, Woman, Catholic, Yes.

Interval Scale of Measurement

3. Interval/Equal-Interval: Order and equal units. -Example: Achievement test scores (SAT, ACT). -Equal distanced but there is no absolute zero (there is no absence of the variable). -You can put the values in an order and the differences are equal. EXAMPLE: The difference between 1 and 2 would be the same as the difference between 2 and 3. -Age is ratio-scale, but when only given a certain range (I.e. 18-30, it would be interval b/c there is no absolute zero in that range). Same difference between 18 and 20 and 10 and 12 = 2 years.

Statistics and Data

Mathematical procedures used to organize, summarize, analyze, and interpret observations Numbers assigned to observations according to rules, called 'scores' or 'raw scores' Example: Age; religious affiliation: you can assign numbers to these categories -Allows quantitative analysis

Population parameter symbols vs. Sample statistic symbols

Population Parameter: Mean = μ Variance = σ^2 SD = σ Sample Statistic: M SD^2 SD

Measures of Variability: Variance

Variability: How spread out the scores are in a distribution. Does it VARY? -The average of each score's squared difference from the mean. -Value can be 0 (no variability) or greater than 0 (there is variability). -A negative variance is meaningless. You will never have a negative number! There is no negative variability. -Variance is a preferred measure of variability because all scores are included in its calculation (similar to the mean - rooted in the mean, every score is included). -The average squared deviation from the mean. 1. Find the mean 2. Subtract the mean from each raw score 3. Square each of these deviation scores (sum after you subtract the mean from each raw score). 4. Add up all the squared deviation scores. This is the sum of squares. 5. Divide the sum of squared deviations by the number of scores (N). SD^2 = E (X-M)^2 / N -Take the mean and subtract it from each score in our data (because you do parentheses first), then square every deviation score, then add those together to give us our numerator. Divide by N in our denominator to get our variance. -Why do you square the negative deviation scores? Because that will give you a positive number! Just adding the deviation scores together would give you 0! That is because numbers will be on both sides of the mean, so with the nature of the mean being the middle score, the negatives would cancel out the positives.

Finding the Percentages of People who Fall above/below a certain z-score HIGHEST POSSIBLE RAW SCORE IN TOP _%, GO TO + Z-SCORE AND GO TO TAIL. HIGHEST POSSIBLE RAW SCORE IN BOTTOM _%, GO TO - Z-SCORE AND GO TO TAIL.

WHEN TO ADD 50% to your PERCENTAGE in the normal curve table: a. If you are finding the % below a positive z-score (look to mean to z column) b. If you are finding the % above a negative z-score (look to mean to z column) WHEN NOT TO ADD 50% a. If you are finding the % above a positive z (look to tail to z column) b. If you are finding the % below a negative z (look to tail to z column) -Example problems: M=100, SD=15 (IQ is standardized so this will always be true) (a) Raw score = 125, how much above? 125 - 100 / 15 = z of +1.67, TAIL TO ZO COLUMN, no 50% -Person A would be in the 95th percentile due to only 4.75% of scores being above their score. ______________________________________________________________ (b) 95, how much above? 95 - 100 / 15 = z of -.33, MEAN TO Z, add 50% -Person B would be in the 37th percentile because about 63% scored higher than them. ____________________________________________________________ (c) SCORE NEEDED TO BE IN TOP 5%. Put percent on normal curve. Put 5% in the tail, z would be roughly between 1 and 2 SD (positive 1 and 2). Look in table for z to tail of 5, the z would be 1.64. RAW SCORE = 124.6 needed to be in the top 5%. ______________________________________________________________________ (d) Score needed to be in top 55%. Put percent on normal curve. 55% going to the right, notice about 5% goes from the mean to the z. FIND THE MEAN TO Z COLUMN. Look for 5%. 0.13 z-score, raw score of 98.05 needed to be in the 45th percentile (about 45% scored lower than you). _______________________________________________________________________ (e) RANGE OF SCORES to include 95% of test takers in the middle range. Split tails to have 2.5%, the positive and negative z-scores will be between 1 and 2 SDs. Look in tail to z for 2.5. + or - 1.96, plug in for raw scores. Need between 70.6 and 129.4 to be in the 95% of middle-ranged IQ scores.

Changing a z-score to a raw score

X = (Z)(SD) + M -Example: You were in the 99th percentile. You can take that information to think of it as a z-score and figure out what a person's raw score is. -The DISTRIBUTION of z-scores has a mean of 0 and a SD of 1. -This is not true for raw scores where the data can change the mean and SD, but for ALL z-scores, the M=0, SD=1. We like z-scores because they are STANDARDIZED this way. -Positive z = score above mean -Negative z = score below mean -0 z = score of mean -Most of the time, just because your z-score is negative does not mean your raw score will be. It depends on the data.

A. CONTINUOUS OR DISCRETE B. QUALITATIVE OR QUANTITATIVE C. SCALE OF MEASUREMENT USED Time (in seconds) to memorize a list

a. Continuous b. Quantitative c. Ratio

A. CONTINUOUS OR DISCRETE B. QUALITATIVE OR QUANTITATIVE C. SCALE OF MEASUREMENT USED Weight (in pounds) of a newborn infant

a. Continuous b. Quantitative c. Ratio

A. CONTINUOUS OR DISCRETE B. QUALITATIVE OR QUANTITATIVE C. SCALE OF MEASUREMENT USED Temperature (degrees Fahrenheit)

a. Continuous - can have decimals! b. Quantitative c. Interval - THERE IS NO SUCH THING as an absence of temperature!

A. CONTINUOUS OR DISCRETE B. QUALITATIVE OR QUANTITATIVE C. SCALE OF MEASUREMENT USED Body type (slim, average, heavy)

a. Discrete b. Qualitative c. Nominal

A. CONTINUOUS OR DISCRETE B. QUALITATIVE OR QUANTITATIVE C. SCALE OF MEASUREMENT USED Political Affiliation

a. Discrete b. Qualitative c. Nominal

A. CONTINUOUS OR DISCRETE B. QUALITATIVE OR QUANTITATIVE C. SCALE OF MEASUREMENT USED Type of distraction

a. Discrete b. Qualitative c. Nominal

A. CONTINUOUS OR DISCRETE B. QUALITATIVE OR QUANTITATIVE C. SCALE OF MEASUREMENT USED A college students' SAT score

a. Discrete b. Quantitative c. Interval

A. CONTINUOUS OR DISCRETE B. QUALITATIVE OR QUANTITATIVE C. SCALE OF MEASUREMENT USED Ratings of satisfaction (1-7)

a. Discrete b. Quantitative c. Interval - BECAUSE THE SCALE DOES NOT BEGIN AT 0.

A. CONTINUOUS OR DISCRETE B. QUALITATIVE OR QUANTITATIVE C. SCALE OF MEASUREMENT USED Position standing in a race

a. Discrete b. Quantitative c. Ordinal

A. CONTINUOUS OR DISCRETE B. QUALITATIVE OR QUANTITATIVE C. SCALE OF MEASUREMENT USED Ranking of favorite foods

a. Discrete b. Quantitative c. Ordinal

A. CONTINUOUS OR DISCRETE B. QUALITATIVE OR QUANTITATIVE C. SCALE OF MEASUREMENT USED Number of dreams recalled

a. Discrete b. Quantitative c. Ratio

A. CONTINUOUS OR DISCRETE B. QUALITATIVE OR QUANTITATIVE C. SCALE OF MEASUREMENT USED A letter grade (A, B, C, D, F)

a. Discrete - JUST THE LETTER, NOT THE ACTUAL GRADE AS A NUMBER! b. Qualitative c. Ordinal

Shapes of Frequency Distribution - Kurtosis

a. Normal (Mesokurtic) - Standard Curve - This is what we expect most data to look like if we collect enough of it. b. Leptokurtic (a more peaked curve) - Strong mode in the middle. c. Platykurtic (a more flat curve) - think of PLATYPUS BILL. - Not a lot of variance.

Shapes of Frequency Distributions - Skew

a. Symmetrical: Generally the left and right side look close to the same. Same amount of frequency on either side or roughly the same. b. Positively skewed: THE TAIL goes to the right (the smaller portion). This FD would also skew to the right. c. Negatively skewed: THE TAIL goes to the left (the smaller portion). This FD would also skew to the left. TAIL ON LEFT = SKEW LEFT = NEGATIVE TAIL ON RIGHT = SKEW RIGHT = POSITIVE