SWU 321 Ch 1-3 Arizona State University

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What are the characteristics of a frequency distribution for nominal level data?

FD are constructed directly from raw data with no particular order

Ratio level data

Fixed, absolute, ranked data with absolute zero,

What is meant by a sample?

Gathering data from smaller subset of a population

Variability

Gives an indicator of the amount of variation among the attributes of a variable in a data set. Also called dispersion

Reversing the z score

Gives you the percentiles

Constant

Is the same across all avenues; can vary among studies

Why use percentages instead of frequencies?

It allows groups of various sized to be equally compared (Out of 100)

Covariance

It is not ethical or possible to design studies that can be used to demonstrate that one variable influences the other; we can see it in two or more variables, but cannot say causal relationship, so COVARY is the word. Can help to predict the attribute of one variable by knowing the attribute of the other

What are the 3 types of means?

1) Arithmetic: Add all numbers and divide by the number of Attributes; outliers can distort 2) Trimmed mean: Bottom and top five percent is not calculated. 3) Weighted: Used when computing the average of unequally weighted attributes. You even out unequal Att's for an even comparison

What are the two other used of variability and central tendency?

1) Describe the overall distribution of a variable within a sample or population 2) They make other types of statistical analysis possible

What are the types of statistical analysis that variability and central tendency make possible?

1) Estimate the D of a V within the population 2) Compare D from one sample w/another 3) Compare D of sample to the D of the population it came from 4) Compare V's of 2 data sets 5) Compare simultaneously several V's within research sample or population

Operationalization

1) How will the variables be measured? 2) How will we determine type of intervention? 3) support with professional evidence

Which measure of CT is used with nominal? Ordinal? Interval/ratio?

1) Nominal: mode 2) Ordinal: Mode best choice but ordinal measurements produced by group freq dist use the median 3) Interval/ratio: Median or mean, but it is best to use ethical judgement to ensure accurate representation of the data

What are the two most common ways statistical analysis may be categorized?

1) Number of variables 2) Primary purpose

Conceptualization

1) Selecting the most important variables to study 2) Stating exactly what is meant by each variable 3) why they are important 4) Explain concepts and variables

What are the steps for determining variance?

1) Subtract the mean from each attribute (mean deviation) 2) Square each 1 3) Divide the sum of squared differences by the total number of attributes (Subtract 1 for sample data)

Why use grouped freq dist?

1) Too may or unequal spreads of attributes 2) easier to visualize and comprehend when grouped (10-15/16-20) 3) Too many attributes to list each one (Continuous V and there are a lot of cases)

What is meant by number of variables?

1) Univariate 2) bivariate 3) multivariate

How do research hypotheses evolve?

1) findings on someone else research 2) Own experience 3) literature review

What determines what kind of graph to use to display data?

1) level of measurement 2) Need for clarity

What two things need to be present to determine the z score?

1) mean 2) standard deviation

What is meaningful grouping?

1) type of grouping that reduces the number of attributes to smaller number that can be easily displayed and understood without compromising measurement precision 2) Makes attributes grouping similar to one another and meaningful, they should share similar characteristics 3) Each group must fall into one group and groupings should be mutually exhaustive and exclusive.

What needs to be present for Att's to be normally distributed?

1) when graphed, it will be bell curved and symmetrical 2) M, M, M similar 3) Most attributes fall between -1 and +1 standard deviation from the mean. (A few may fall above 3

Each z score correspond to:

1) z score and 2) percentile rank

What are the steps to figure out SD?

1)List the A for the V in column A 2)Compute the mean of the A in columnA 3) List the mean in columnB 4)Subtract the mean from each A in columnA and list in colunmC 5)Square each A in C and list in D 6)Compute the sum column D 7)Divide the sum by total number of Att (minus 1 for sample data). 8)Compute the square root

What is meant by bivariate and what are they used for?

2 variables are measured; use of statistical tests to determine if there is statistical support for research hypothesis about the relationship between TWO variables

What is correlation?

A relationship among variables in which certain attributes of one variable reflect a pattern of relationships with another

Research hypothesis

A statement describing what the researcher suspects the relationship among variables will be

Binary

A type of dichotomous variable where researcher assigns attrubutes of 0 or 1 for the presence or absence of a variable. (Own car? 1-yes 2-no)

What is a z score?

A way of converting raw scores into standard deviation units, making it possible to compare A's from 2 samples or populations

What is descriptive analysis?

A way to summarize and communicate the most important, salient data. Summarize the measurement of variables into graphs, charts, and descriptive summaries

Positive skew

Bulk of data is at the low end of the scale

Negative skew

Bulk of data is concentrated at the high end of the scale

What is ordinal plus

Able to use final score as numerical data and allows for more mathematical statistical analysis. Distances between numbers are equal

Dummy variable

Allows for transformation into ratio level data

Secondary data

Analyzing primary data for other data

What are the two types of non causal relationships and when are they used?

Association and correlation; used when we are unable to introduce or manipulate the attributes of one variable to examine the effects of the other

What are the characteristics of a frequency distribution for ordinal level data and higher?

Attributes have a logical sequence based on the quantity of the variable

Mesokurtic? Characteristics of?

Bell shaped, normally distributed curve. Measurements closest to the mean are most common. Tapers consistently and gradually. Mode, median, and mean all in about the same place

What is a one-tailed or directional hypothesis?

Can predict variables are related and predict the direction the relationship will take

Continuous variable

Can take on all numerical values, including fractions and decimals

Data

Collected measurements from a research study; before analysis

Cumulative percentage fd?

Combines features of the cumulative freq and percentage distribution tables - displays column for cumulative % for each attribute

What are the features of z scores?

Compared to other scores, converted into percentiles, compared to their respective distributions

Frequency distribution?

Consolidate data sets constructed from arrays

What is an absolute frequency distribution (Simple FD)?

Count number of times an attribute occurs and list them (any level of measurement)

Practical uses of z score?

Curving on tests and standardized measurements - IQ test, SAT's, normal distributions

What is meant by primary purpose of analysis?

Data grouped into two categories: descriptive and inferential statistics

Kurtosis

Degree to which a D is peaked and how much A cluster around the center

What is a parameter?

Descriptive summaries of the attributes of the variables that were measured. (A 20% sample of student data, when summarized: statistics) Form the basis of more complicated analysis. Parameters summarize data from populations and statistics summarize data from samples

Attributes

Different categories a variable can assume (words or numbers)

Data set

Different sets of data within the same study

Variable

Differs among and in measurements - primary focus in statistics

Percentage frequency D

Displays an absolute percentage column on right side; percentage of total number of distribution

Median

Divides an array of Att's into two equal halves. Interval and ratio

Leptokurtic

High degree of A cluster around the center (Mean)

What is percentile rank?

Indicate the % of cases within a certain group whose attributes fall below or above a certain score, this enables us to put attributes in perspective relative to other attributes within the same group

Mean

Interval and ratio

Polygon

Interval/ratio;

How is information different than data

It is the interpretation of that data from a research study

Percentage are useful with _______ amounts of date, but not with _________.

Large; small

Reliability

Level of consistency the test produces

What is nominal data?

Lowest level, categorical data, Must have two or more attributes or would be a constant, clearly exhaustive and mutually exclusive, numbers do not hold any value

Confounding variable?

May contribute to variations in the dependent variable

What MOCT is most commonly used in social work and what makes it vary?

Mean: normally distributed Median: skewed

What is meant by univariate and what is it used for?

Means one variable; Helps to visualize certain trends in the measurements of a single variable that might otherwise be hard to discern or comprehend

What is multiple indicator?

Measure a single variable multiple ways to decrease human error, bias, ect.

What LOM is best when there are outliers?

Median

Platykurtic

More flat polygon, A heavy at tales

Interval

No absolute zero, rank order and equally spaced; criterion/continuum, attributes indicate how far apart values are from each other. Difference between intervals matter and can be measured. Ranked data with equal distances

Can SD be used with skewed data? Why?

No, the distance between standard deviations are not even

Pie charts? Level of measurement

Nominal

Explain ordinal data

Nominal plus quantitative quality, social class, education, order a race finishes, intervals not equal, values ranked in hierarchy, No "true" numerical values, rank in order, No mathematical quality

What are the levels of measurement?

Nominal, ordinal, interval and ratio

List possible questions for nominal, ordinal, and ratio levels of measurement if you want to know the hours the individual worked the prior week

Nominal: Did you work last week? Ordinal: 10-15 16-20 21-25 26-30 Ratio: How many hours did you work last week? _____

How is standard Normal Distribution relevant?

Normally distributed V's do not have to fit standard normal D's perfectly, but do need to come close to be normally distributed

Frequency

Number of times an attribute occurs within a data set

________ on polygons are also the __________ of Att's that fall within respective distances from the ________ of a normally distributed __________ or __________ level of measurement.

Numbers / percentages / mean / interval / ratio

Causal

One variables attributes cause or contribute to the other variable

What are the 3 forms of research hypothesis?

One-tailed/directional, two-tailed/nondirectional, and the Null

Dichotomous variable

Only two attributes: (Yes No) (Male Female)

Array?

Ordering every attribute of a variable that occurred within the raw data from low to high: automatically generated with software

Cumulative FD and type of data

Ordinal or higher; counts a running total of how many

What is association?

Predicts certain attributes of one variable will be found with another

Validity

Present only when the measurement is considered both reliable and consistent; it measures what it is supposed to

Why use a 5 number summary and what are they?

Provides a more complete image of the list measurements of a V. It reports the minimum A, 25th percentile, 50th percentile (median), 75th percentile, and the maximum Att

How to calculate z score

Raw score minus mean divided by the standard deviation

What is meant by data reduction?

Reduce large amounts of date into simple and more understandable info without distorting or losing overal meaning

Datum

Singular form of data

Explain multivariate:

Sort the interrelatedness of three or more variables; sort complex relationships among variables that are not simple cause and effect ; examine relationships between and among variables similtaneously

Variance

Sum of squared deviations from the mean and divided by number of cases

asymptotic

Tales of D get closer and closer to zero, but never touch the axis

Standard Deviation

The amount of variance within a data set

Mode

The attribute that occurs most frequently; most unrestricted and can be used with all LOM, but does not describe interval or ratio very well

Interquartile Range

The data from the 25th percentile to the 75th or the middle 50%

Skewness

The degree to which a D of V is not symmetrical (polygon)

Range

The distance between the maximum and minimum numbers plus one. Easily distorted by outliers

Standard deviation and 5 characteristics

The square root of the variance. 1)Frequent in quantitative research. 2)useful for describing the variability of research. 3)Use with interval/ratio data. 4)Uses all case attributes. 5)Tells the extent the attributes cluster around the mean. determine where a given attribute falls relative to other Att's (percentile)

Null hypothesis

The variables are unrelated

Central Tendency?

The way data is bunched around the center of the D

Standard Normal Distribution? Features?

Theoretical D based on the normal curve. Perfectly symmetrical, rarely happens, divided into 6 equal units. Asymptotic, bell shaped, M, M, M all fall approx same place

Why use a box plot?

To display the central tendency and dispersion of the A's of a V. Also displays outliers.

Bimodal

Two attributes occur most frequently

How to combat human error?

Use multiple data sets to measure one variable (multiple indicators)

Inferential statistics

Used when data are collected from a sample rather than a population. Sample statistics are estimates of population parameters

Bar graphs and line diagrams? Level of measurement and features?

Useful for displaying freq list for nominal level / Bars of equal width that do not touch; one for each attribute. Height reflects freq and order is abrituary

Mean deviation

Uses all attributes; the average amount the attributes differ/deviate from the mean. Add all absolute sums of deviations and divide by the total number of attributes

If we were measuring self-esteem, what would be the variable, indicator, attribute, and data source?

Variable: self esteem; Indicator: Self-esteem questionnaire (ISE); Attribute: Scores on questionnaire; Data source: Clients complete the ISE on posttest-pretest

What is a two-tailed or nondirectional hypothesis

Variables are related but do not predict the direction of their relationships

Non causal

Variables do not cause each other but have an identifiable pattern

What is the relevance of a null hypothesis?

We try to prove that the null hypothesis is false because you cannot prove definitively that the other two are absolutely true.

Discrete variable

Whole numbers; Only finite number of attributes (SAT scores)

What is the horizontal line of a graph? Called the _________. Displays _________

X axis / abscissa / attributes

What is the vertical line of a graph? Called the ________. Displays ___________

Y axis / ordinate / frequencies

Any z score is the _________ of ________ _________ that an attribute falls from the mean. They can be _______ or _______ the mean

number / standard deviations / above / below

Histogram

ordinal or higher / bars touch / ordinal - equal width / interval or ratio - width varies


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