AD RESEARCH FINAL: Descriptive Statistics
Variable B has to change at the same time as Variable A
Correlation
"R" value Indicates the strength of a linear relationship
Correlation Co-efficient
- Study a group of data and inferring the sample projects onto the larger population - More powerful than descriptive - Process of statistical inference
Inferential Statistics
Used to make estimates of how likely it is these statistics represent the population
Inferential Statistics
Simplest technique for analyzing nominal variables in bivariate ways
Cross Tabulation
Technique for studying the relationships between variables
Cross Tabulation
simple, but important technique for studying the relationship between variables. (Percentaging a Table- Rule for Percentage Calculations: Always calculate percentages in the direction of the causal factor (antecedent) and across the effect (criterion) factor).
Cross Tabulation
Bell-shaped - Positive Skew - Negative Skew -
Curves and their shapes
- Used with interval and ratio - Average - Most powerful
Mean
- Dispersion measures describe the way in which the scores are spread out about a central point. - The range is the difference between the highest and lowest scores in a distribution of scores. - Variance provides a mathematical index of the degree to which scores deviate from, or are at variance with, the mean.
Measures of Dispersion
Describe the way in which the scores are spread out about a central point
Measures of Dispersion
- Midpoint of distribution - Used with interval and ratio
Median
The main purpose for summary and descriptive methods of quantitative analysis are to reduce data and to enable us to see patterns and trends. You run the stats. If you find something important, you highlight it in the report. You always start with univariate statistics and analyses. Then you move on to whatever bivariate analyses will reveal something important about the research problem.
Methods
- Used only with nominal level of measurement (weakest)
Mode
Means that 1 set of variables increases while the other set or sets decreases
Negatie Correlation
Tool that enables us to make inferences from samples to populations
Normal Curve
- Has a sign indicating direction of relationship - Number indicates strength of relationship - Meaningful value when squared
Pearson's Product Moment Correlation
When 2 or more sets of variables gain in value together, not necessarily at the same time.
Positive Correlation
What kind of technique is a thematic apperception test?
Projective Technique
Data Distributions- (an unordered array of responses), Frequency Distributions- (a typical frequency distribution table consist of two columns -the possible values of the variable in the form of categories and the number of occurrences, or frequency, of each value). "Collapsing" the Data- (condense the data)
Quantitative Analysis
What is the most common method for determining correlation
Regression Analysis
The probability in the area below a normal curve
Rejection of the null hypothesis
What has to be at least ordinal level for the median to be a meaningful measure of central tendency?
A distribution of numbers
Where does the independent variable go in a contingency table?
At the top of a cross tabulation of contingency table
Numerical expressions of the degree to which two variables change in relation with one another (covary) are called measures of association or correlation. Typically, the variable presumed to be antecedent is designated "X" and the criterion "Y".
Basic Correlation Statistics
- Normal distribution of scores - Cluster around the mean
Bell-Shaped Curve
"What can we do with that data using bivariate analyses that help us address the original research problem at greater depth?"
Bivariate
use a scatterplot
Bivariate
Provides assurance that any random sample statistic comes from a population of statistics that form a normal curve around the true population parameter.
Central Limit Theorem
- Values identified by "x" - Used to measure data at a nominal level - Used to test distribution frequency to single-variable or to compare groups
Chi-Square
Examples of Bivariate Statistics?
Chi-Square Correlation ANOVA
The level of statistical confidence that is built into the sample
Confidence Level
Means that two or more sets of variables are related to one another at the interval or rational level
Correlation
What is another form of determining correlation?
Significance
The process of estimating parameters from statistics we always study samples instead of populations
Statistical Inference
The arithmetic average. The most power, but comes at a price.
The Mean
The midpoint of a distribution
The Median
The score or scores occurring most frequently
The Mode
All projective techniques share what element in common?
They are all based on the projective hypothesis
The square root of the variance of a distribution of numbers is the standard deviation
True
True or False? A distribution of numbers has to be at lease ordinal level for the median to be a meaningful measure of central tendency?
True
True or False? A distribution of numbers has to be at least ordinal level for the median to be a meaningful measure of central tendency
True
True or False? All quantitative data, regardless of level of measurement, can be analyzed with frequency distribution tables, proportions, percentages and ratios
True
True or False? Frequency distributions are one method for presenting data in descriptive statistical analysis
True
True or False? If there is an even number of scores or observations in a distribution, you use the mean of the two middle scores to calculate the median.
True
True or False? If you want to know how well the mean represents a distribution of numbers, you should also look at the standard deviation
True
True or False? Inferential statistics are more powerful than descriptive statistics.
True
True or False? Measure of dispersion can be used to reveal the "shape" of a distribution of scores or numbers
True
True or False? Measure of dispersion could be used to reveal the shape of a distribution of scores or numbers.
True
True or False? The chi-square statistic and test for significance is typically used with data measured at the nominal level.
True
True or False? The mean is sensitive to extreme values and should be supplemented with another measure of central tendency when there are extreme values in a distribution.
True
True or False? The term that's used to describe whether a distribution's curve is tall and peaked or short and flat is called "kurtosis"
True
True or False? Unlike the mode and the median, the mean takes into account all the values in a distribution making it especially sensitive to the effects of extreme scores
True
True or False? You could reduce data using a frequency distribution table.
True
Once you've collected your data, you begin with univariate analysis. One good way to begin is by looking at the items you have that measure related concepts and variables.
Univariate
Measures of central tendency and dispersion are examples of what?
Univariate Statistics
- Single variable - Simplest form of data tabulation - Involves the presence of frequency and distribution
Univariate Variable
Probability level is usually expressed by a lowercase _____?
p (in italics) followed by a less that or equal to sign and a value
The sum of all scores in a distribution of numbers, divided by the number of scores is the definition of _____
the mean
What are examples of bivariate statistics?
- Chi Square - Correlation - ANOVA
What are examples of univariate statistics?
- Measures of central tendency - Dispersion
The different measures of dispersion
- Range - Variance - Standard deviation
Quantitative Analysis
- Starts with little background info - Objective - Deductive and logical - Provides generalizations - Sample size is essential - Goal is to classify and count - Uses measuring instruments
What are some data tabulation issues?
- hand tabulation is inefficient - human error while recoding - lose sight of micro-level trends - average of data does not show the entire picture - collapsing data lessens precision of analysis
o Hand Tabulation: unless your data set is especially small, hand tabulation is likely to be inefficient and time prohibitive. If you have a simple questionnaire, and you are looking for a very specific set of data, then hand tabulation may be efficient. o Computer Tabulation: It is convention for each row to represent a unit of analysis and each column to represent a variable. Data are entered as close to the raw form as possible. Computer programs can recode variables without error while human error is almost assured in recoding large data sets. o The Single Variable: The simplest form of data tabulation involves a single variable and is often called univariate, meaning one variable. At the most basic level, it is helpful to know how many times each option was chosen for the variable. How many were male or female? How many people strongly agreed or disagreed with the statement. o Getting A Good Look At The Data: There is no one way to tabulate data. No matter how data are tabulated, there will be some consolidation and lack of clarity. As you step back, you can begin to see patterns in the data; however; you also will begin to lose sight of micro-level trends in the data. In this sense, data tabulation is about the processing of coming to understand your data rather than simply going through a checklist.
Data Tabulation and Findings Presentation Issues
A variable that goes down the side of a cross tabulation table and whose values are in the rows should be the
Dependent Variable
- Range - the difference between the highest and lowest scores in a distribution of scores - Variance - provides a mathematical index of the degree to which scores deviate from, or are at variance with, the mean. - Standard Deviation - overcomes the problem of variance not being calibrated in the same units as the original data by taking the square root of the variance.
Dispersion
True or False? A cross tabulation is used when one nominal-level variable and one interval-level variable need to be analyzed simultaneously to see if there's a relationship between them
False
True or False? A cross-tabulation is used when one nominal-level variable and one interval-level variable need to be analyzed simultaneously to see if there's a relationship between them
False
True or False? If you wanted to test more than two mean scores you'd have to use a t-test instead of ANOVA
False
True or False? It is generally assumed that 100% of the scores in a distribution of numbers will fall within plus or minus two standard deviations from the mean, especially if the distribution is believed to be normal
False
True or False? It is generally assumed that 100% of the scores in a distribution of numbers will fall within plus or minus two standard deviations from the mean, especially if the distribution is believed to be normal.
False
True or False? Measures of central tendency and dispersion are examples of bivariate statistics.
False
True or False? Measures of central tendency and dispersion are examples of bivariate statistics?
False
True or False? The Median and Mean can be used to analyze all four levels of measurement
False
True or False? When testing for Mr. Pearson's r for statistical significance, the null hypothesis is almost always that the correlation between the two variables in the population is greater than .05
False
What is the most important feature of a normal curve?
Fixed areas below the normal curve represent the frequency of the scores of values of a variable that fall in those areas. Allows us to know how variables vary without measurement
Are summary descriptive statistics a way to reduce data?
Yes. - Measures of Central Tendency - Mean, Median, Mode