Statistics

The Ratio Level of Measurement

characterized by the presence of an absolute zero on the scale. The zero means the absence of any of the trait that is being measured. *tricky in behavioral science

X

each individual score in a group of scores

Best central tendency strategy if the data you are measuring is at a high level (interval/ratio)

is to use the mean (the most often used measure of central tendency).

Interval Level of Measurement

1+1=2 A test or an assessment tool is based on some underlying continuum such that we can talk about how much more a higher performance is than a lesser one. *The intervals or spaces or points along the scale are equal to one another. Not just the actual math that determines whether there are equal intervals: it is assumptions about the underlying concept being measured -One thing always represents another thing.

How do you solve for the Mean?

1. List the entire set of value in one or more columns. These are all the X's 2. Compute the sum or total of all the values 3. Divide the total or sum by the number of values *Add up scores and divide by the Total # (n)

Steps to solve for the Median

1. List the values in order, from either highest to lowest or lowest to highest. 2. Find the middle-most score. That's the median. Even Number: When there is an even number of values, the median is simply the mean of the two middle values (Sum of two numbers divided by two). Middle number is the same: The median is the same as those middle numbers

Scales of Measurement

1. Nominal: discrete scale, named categories. JUST categories. MODE 2. Ordinal: Discrete scale, ordered hierarchy, ranking system. Allows for MODE but adds rank/ordered hierarchy and thus MEDIAN 3. Interval (most likely used in psychology)- Continuous scale, each point reflects the same difference as per the point above and below, however the range (data points) is arbitrary. Ex. #line *MODE MEDIAN AND MEAN adding decimals, distance and specifics. This scale lacks absolute zero. 4. Ratio- Continuous scale, each point reflects the same difference as per the point above and below. *contains absolute zero

Difference between a capitalized letter and a lower case letter in statistics

Capitalization refers to population Lowercase refers to samples

Three guidelines for deciding which central tendency to use...

1. Use the mode when the data are categorical (Nominal) in nature and the people or things can fit into only one class, such as hair color, political affiliation, neighborhood location, and religion. (Mutually exclusive) 2. Use the Median when you have extreme scores and you don't want an average that is misleading, such as when the variable of interest is income expressed in dollars. 3. Finally, use the mean when you have data that do not include extreme scores and are not categorical, such as the numerical score on a test or the number of seconds it takes to swim 50 meters.

Statistics

A branch of mathematics designed to summarize, organize, and interpret data or information Describes a set of tools and techniques that are used for describing, organizing, and interpreting information or data. -data is collected, organized, summarized, and then interpreted. -Organizes information we've collected and then lets us make certain statements about how characteristics of those data are applicable to new settings. -Descriptive and inferential statistics work together.

Data Set

A collection of Data

Data point

A point representing a lack of what was measured

Sample

A smaller group of data. A portion or a subset of a population. The selection from the population that was tested, who we hope can generalize to represent the population. (Statistics are the numbers that relate to a sample)

Measures of Central Tendency

Aka: Averages. 1. Mean 2. Median 3. Mode

First step after you collect data...

Begin to understand all the bits of information using single numbers to describe data. Easiest way is to compute the average through one of the measures of central tendency: Mean, Median, Mode

Variable

Condition, characteristic that can change, or can have different values.

Inferential Statistics

Make a decision, inferences about larger data sets/groups. Types: 1. Parametric statistics (assumes probability distribution) 2. Non-parametric statistics Often the next step after you have collected and summarized data. Used to make inferences based on a smaller group of data about a larger group.

Operational Definition

Defined in such a way as to describe how we will measure the construct 1. Discrete Variable: Hard boundaries between groups, dichotomy, categorical 2. Continuous Variables: Range, spectrum, degrees -continuous can be redefined as discrete, but some information might be lost. The reverse can't occur.

Levels of precision in central tendencies

Mean, Median, Mode

M

Median

Σ

Sigma or summation sign. Tells you to sum up or add together whatever follows it.

M

Median. -Finding the ranked center. Place in the ranked order then find middle. If it is an even number take the mean of the 2 center #'s Even: Find n/2 for ranked position Odd: Find n/2 and round up *because the median is based on how many cases there are, and not the values of those cases, extreme scores (outliers) only count a little.

Mean

Most common type of average. The Sum of all the values in a group, divided by the number of values in that group. X̄ =ΣX/n Centermost point where all the values on one side of the mean are equal in weight to all the values on the other side of the mean. very sensitive to extreme scores. An extreme score can pull the mean in one direction or another and make it less representative of the set of scores and less useful for which the mean is being computed. *aka arithmetic mean (sum of deviations is equal to zero) X̄= associated with samples of a part of a population mu= entire population as a whole

Data (datum;singular)

Multiple observations

Scores

Observations from one person

Ordinal Level of Measurement

Ordered, Rank. Don't know exact distances between ordered numbers but we do know 1 is better than 2 and 2 is better than 3 and so on just not by how much. "Any order is fine with me".

What do the scales of measurement/rules represent?

Particular levels at which outcomes are measured. 1. Any outcome can be assigned to one of four levels of measurement 2. Levels of measurement have an order. Least precise nominal, ordinal, interval to most precise ratio. 3. The higher up the scale of measurement, the more precise the data being collected, and the more detailed and informative the data are. We can always make simple rich/poor distinctions of lower classifications after we get how much money they earn (higher ratio information). 4. More precise scales contain all the qualities of the scales below them. Interval Scales include the characteristics of the ordinal and nominal scales.

Descriptive Statistics

Summarizes the data. Types: 1. Measures of central tendency 2. Measures of dispersion (measures of variability) 3. Measures of relationship (correlations) Used to organize and describe the characteristics of a collection of data. Collection is called a data set/data/sample (a collection of data that you have in front of you). -descriptive statistic that identifies the variable is called the mean. -descriptive statistic that summarizes the most frequent choice is called the mode. *used for anytime there are more than just a few people or things you want to describe.

Experimental Method

The ONLY methodology that can demonstrate cause and effect. 1. Multiple groups (minimum of 2) 2. Group Make-up is identical (to control for extraneous variables) 3. One group is unchanged, other group(s) are manipulated 4. Independent Variable: Each manipulation (multi-leveled) something changed by the experimenter. a)Experimental conditions: Receive manipulation b)Control Conditions: Remains unchanged by manipulation 5. Dependent Variable: measured outcomes. *confounding variable, extraneous variable, third variable effect...something other than the manipulation that may have been the cause of a measured outcome.

Sampling Error

The difference between the sample statistic and population parameters.

Why use the median instead of the mean?

The median is insensitive to extreme scores, while the mean is very sensitive to outliers. When you have a set of scores in which one or more scores are extreme...use the mean.

Median

The midpoint in a set of scores. It's the point at which one half, or 50%, of the scores fall above and one half, or 50%, fall below.

Mode

The value that occurs most frequently. -Doesn't have to exist. Multimodal frequencies do exist. -can use zero or several scores. Doesn't have to exist. It the most common number or item. Ignores outliers completely. Used for categories. -most general and least precise measure of central tendency, but it plays a very important part in understanding the characteristics of a sample of scores. Warning: Don't select the number of times a category occurs instead of the LABEL of the category itself. The mode is the value that occurs most often not the frequency. -If the frequency is the same for all the values then there is no mode -If more than one value appears with equal frequency, the distribution is multimodal or bimodal (two modes) or trimodal.

Constructs

What we are looking at: A concept.

X̄

X Bar is the mean value of the group of scores. MEAN

Weighted Mean Formula

X̄= Σ(xw)/Σw *instead of each data point contributing equally to the final mean, some data points contribute more weight than others. Use the weighted mean for two reasons 1. Apply when range of scores is narrow but large data set is present to make it easier to manage 2. Shifting from average composite score *When a data set contains several repeated values, a weighted mean may be used to simplify the calculation (instead of adding each value together). -A weighted mean may be used to calculate the mean of multiple data sets where only the mean and frequency (n) of each data set is known. Key: x=score w=frequency x*w= score multiplied by frequency

Population

all the occurrences with certain characteristics. Samples should represent their populations well. Inferring from a sample to a population makes a lot of sense if the sample represents the population. -every individual that the research pertains to. *Parameters are the numbers that relate to or describe a population in greek letters

Nominal level of measurement

an outcome that fits into only ONE class/category. Least precise level of measurement -Mutually exclusive category. If it is in one category it cannot be in another. -No direction to the difference. just that there is one. Ex. Male/Female, Ethnicity, Political Affiliation "A rose by any other name": Nominal means Name.

n vs N

n represents the sample size for which the mean is computed N represents the population size

Data Points

observations

Which measure of central tendency you use depends on...

scale of measurement that the characteristics of the data are in, the type of data that you are describing, which in turn means at what level of measurement the data occur. Mode: a measure of central tendency for qualitative, categorical, or nominal data: racial group, eye color, income bracket, voting preference, and neighborhood location). Mean & Median: with quantitative data such as height, income level in dollars (not categories), age, test score, reaction time, and number of hours completed toward a degree.

n

size of the sample from which you are computing the mean, the number of scores.

Measurement

the assignment of values to outcomes following a set of rules. Results: Different scales used: Nominal, ordinal, interval, and ratio. Outcome: anything we are interested in measuring

Average

the one value that best represents an entire group of scores