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SOCIA 2502 - Study Guide - Midterm

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1Stats Midterm Study – Miranda Moore Lecture 1 Statistics and social justice ∙ Document trends ∙ Explore marginalisations ∙ Dissemination ∙ Evaluating effectiveness of programs and policies ∙ Needs assessments for program design ∙ Justifying funding ∙ Identifying gaps in research Positivism ∙ Social behvaviour can bIf you want to learn more check out in chemical notation, the symbol ca2+ means

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e studied and understood in a rational, objective and scientific matter Post-positivism ∙ Science subjugates knowledge ∙ New approaches to social work knowledge are important to “install the client as an important site of knowledge” Interpretivism ∙ Critiques of positivism o Limit the multiple voices that can contribute to the construction of social work knowledge o The rigor and rigidity of experimental methods cannot account for the “complexity of human relations and interventions” Data ∙ Resultes obtainted before analysis Information ∙ What we have when we have analysd and interpreted the results Conceptualization ∙ Defining the variables in a study Operationalization ∙ The methods used (ex. The questions we develop) to measure the variable Reliability ∙ Consistency of measurement (over and over) Validity ∙ How well the measurement represents what we want to know NOIR Nominal ∙ Mutually exclusive categories 2∙ No order or rank, Ex. Are you employed? Ordinal ∙ Classifying observations that are mutually exclusive and have an inherent order to them ∙ An example is level of education Interval ∙ Classifying observations that are mutually exclusive and have an inherent order and have equal spacing between categories. ∙ Example – temperature, time Ratio ∙ Have inherent order, mutually exclusive, equal spacing and absolute zero ∙ Income, age, grade Lecture 2 Epistemology ∙ How we know what we know Empiricism ∙ Closely linked to positivism ∙ Belief that only knowledge based on direct observation through the sesnse can be accepted as a scientific fact Aristotle ∙ Commonly considered to be the fisr empiricist and is generally creditied with being the father of modern science ∙ The natural sciences such as physics and biology and the human sciences, such as politics and ethics, have the same level of validity as mathematics Liberalism ∙ Valued o Religious tolerance o Commerce and industry o Middle class rather than the aristocracy or the church o Equality of individuals o Importance of education o Democracy, not existing authority Rene Descartes ∙ I think therefore I am Thomas Hobbes ∙ Materialist ∙ Founder of britis empiricism John Locke 3∙ Father of empiricism ∙ Tabula rasa = blank slate ∙ All knowledge is derived from experience George Berkeley ∙ The only reality is the mind David Hume ∙ Reductionist and mechanistic view of the mind ∙ The mind is the flow of ideas, memories, imagination and feelings Britis Empirisit Summary ∙ By giving such prominence to primary perceptions and minimizing the existence of even simple concepts of knowledge, the British empiricists radically changed the course of Western philosophy. Feminist Empirisism ∙ Linda Jean Sheperd ∙ Until recently the dominat view of the western scientific world, was that only men possessed the necessary qualities to engage in science ∙ Accepts the basic principals of traditional empiricism – that only knowledge based on direct observation through the senses should be accepted as scientific fact ∙ Science is about formulating hypothesis to test against experience ∙ Science is not value free: values cannot be screened out by the scientific method Feminists empiricists on individualism ∙ Individualism holds that knowledge is only achievable by a fully autonomous and separate individual and rejects the notion that social factors should play a role in the production of knowledge. ∙ social factors are both relevant to, and among the causes of, knowledge ∙ social location of the knower is crucial to what they know Lecture 3 Stages of the research design 1. deciding what topic/variables to study 2. conceptualization (define variables) 3. operationalization (develop questions) 4. pilot the method 5. revise 6. implementation Types of statistics we can produce ∙ Descriptive statistics: summarizes the characteristics of the sample according to one or two variables (next two weeks) o Univariate (income distribution) 4o Mean, median, mode, range, SD ∙ Inferential statistics: allows us to make inferences or generalizations about the population using data from the sample (later in the semester) o Bivariate (age and income) o Independent t tests, paired t test, chi-squared, correlation, regression o Also multivariate (age, education and income) o Chi square, ANOVA, multiple linear regression Frequency distribution ∙ A display of the number of times eac value appears when we have measured a particular variable ∙ Examples of frequency distributions: o An array o An absolute frequency distribution o A cumulative frequency distribution o An absolute percentage distribution o A cumulative percentage distribution Absolute frequency distribution ∙ Table that shows the number of times each value occurs in that data set ∙ This can be used for ALL levels of measurement Cumulative Frequency Distribution ∙ This provides the cumulatice totals of the values categories ∙ As this requires an order to the values it can only be used with ordinal, interval and ration data Percentage Distributions ∙ Absolute percentage distributions ∙ cumulative percentage distrutions Absolute percentage distribution ∙ a table that shows each value as a percentage of the data 5∙ can be used with ALL levels of measurement Cumulative percentage distribution ∙ this provides the cumulative percentages of the value categories ∙ as this requires an order to the values it can only be used with ordinal, interval and ratio data Grouped Frequency distribution ∙ can use the same frequency tables as with raw data (AFD, CFD, APD, CPD) but now you have grouped values together ∙ if you are working with a large data set, it is sometimes easier to visualize and comprehend the meaning of the data if you group the values ∙ we see this often when looking at income ∙ nominal values can be groups together IF it makes sense (countries into regions, programs into faculties) Bar graphs ∙ nominal and ordinal data ∙ bars of equal width and do not touch; this is to acknowledge that the data are qualitive in nature with values at the nominal or ordinal level Pie Chart ∙ effective for fewer categories Histogram ∙ data must be interval/ratio level ∙ similar to the bar graph except the bars touch ∙ the width can vary is the categories size varies Frequency Polygons ∙ similar to histograms except that instead of a bar we use a dot ∙ normally used to display data at interval/ratio level Scatter Plots ∙ display the relationship between two variables ∙ the reults on two test scores measuring similar traits or the relationship between number of treatment sessions and the score on a phsycological test Lecture 4 Order of operations BEDMAS 6Squares ∙ to square a number simply multiply it by itself Square Roots ∙ taking the square root of a number is the opposite of squaring a number Nominal data – uses mode Ordinal data – both mode and median Interval/ration – with a skewed distribution (such as income distributions) the median is often used. Normally distributed: mean is used most often Variability ∙ measures of variability can tell us about the degree of dispersion or the degree of variation among the values ∙ variability is also called dispersion ∙ three measures f variability that we will consider: o range, variance and standard deviation Range ∙ take the highest number minus lowest, plus 1 Variance and standard deviation ∙ helps us understand how much the data points vary: how spread out they are around the mean ∙ standard deviation o most commonly repored measure of variability o used much more than variance, but we need variance to get standard deviation o mean and standard deviation very ften reported togehre in research literature and research reports Calculating variance and SD ∙ the variance is the sum of the square deviations from the mean, divided by the number of values minus 1 ∙ the SD is the square root of the variance 7Lecture 5 Inferential statistics ∙ draw conclusions about a population based on a sample ∙ test relationships between two or more variables o ex. Will a change in the independent variable lead to a change in the dependent variable? Probability approach ∙ each individual within the population of interest had an equal chance of being selected ∙ also called random sample ∙ allows us to carry out inferential statistics Basic Laws of Probability ∙ probability is represented by the letter p ∙ expressed in a range from 0 to 1 Addition Vs Multiplication Rule Addition when its ONE event Ex. Whats the chances of getting a queen, jack or an ace in a deck of cards Multiplication used when you have MORE than ONE event Why should we care? Probability and Social Justice ∙ the “numbers” are peoples life chances The normal distribution 8∙ it determines which kinnds of analysis we can do and the trust we can place in the results ∙ abstract ideal Kurtosis ∙ is the degree to which a distribution is peaked as opposed to flat, or the degree to which values cluster around the centre as opposed to being more heavily concentrated at the tails ∙ three different types Skewed Distributions Positive Skewness ∙ tail to the right Negative skewness ∙ tail to the left Z scores ∙ also called standard scores ∙ allow us to make direct comparisions on measurments taken from two diferent groups by working out percentiles ∙ a Z score of 0 means the element/value/data point is identical to the mean 9∙ a Z score of 1 means the element/value/data point is one standard deviation from the mean Calculating z scores ∙ step 1: find the difference between the raw score and the mean ∙ step 2: divide this by the standard deviation Z = Converting Z scores to percentile scores ∙ the z score tells us where a value fits in a normal curve (how many standard deviations it is from the mean) ∙ by using a z table you can convert z scores into percentiles ∙ use the table ∙ then, if the z score is positive you add the number to 50 ∙ if the z score is negative you then subtract the number from 50 ∙ this gives you the percentile 1011Lecture 6 What is hypothesis testing? ∙ Determining if there is a relationship between two variables ∙ Important for: o Program evaluations o Social justice: what are the causes of social justice? How can we address causes to prevent problems from happening? Classic Experimental Design ∙ Allows you to prove that your intervention/program (the independent/causal variable) caused an improvement in the outcome (the dependent/effect variable) ∙ Also called pretest-post test control group design\ ∙ Three conditions o Probability sampleing (random sample) o Experimental group o Control group Hypothesis testing for classic experimental designs 3 criteria to explain causality 1. The two variables must be empirically linked to one another 2. Cause must precede the effect in time 3. The relationship between the factors cannot be explained by other factors. You need to demonstrate that there are no alternative explanations for any relationship found 12Alternative Explanations ∙ Three other types of explanations exist 1. Rival hypotheses 2. Research design flaws 3. Sampling error Rival hypothesis ∙ A third variable can explain the relationship ∙ Maturation: any change in the participant over the study o Boredom o More education, become a parent, inherit money o Community changes ∙ Attrition: participants are lost from the sample over time o Unwillingness to continue, unable to contact Research Design Flaws: Measurment Error ∙ Systmatic error: not a valid measure ∙ Random error o Mood or health chanes on part of respondents o Researcher error such as input error into SPSS o Unclear terminology ∙ Measurement bias 13o Biased wording o Social desiability o Cultural bias or translation problems ∙ Sample bias o Ex an anger management group could be court mandated or voluntary Sample error ∙ Sampling error is the concept that no matter how careful our design, there is a natural tendency for any sample to differ, if only slightly, from the population from which it was drawn, especially if the sample is small and it may not really represent the population from which it is drawn. ∙ So it is possible that the results we have found are due to chance (probability) Refuting sampling error ∙ There are two ways to show that a relationship found between two variables was unlikely to have been caused by sampling error o Replication o Inferential statistical analysis Using inferential statistics to address sampling error ∙ Based on data drawn from a single study ∙ Cheaper, more practical ∙ If we rigorously follow certain scientific procedures to test a research hypothesis, we can arrive at the same conclusion Statistical Significance 14∙ The acceptance level is 95% (0.95) in other words, we are OK with a 5% chance of error P Values ∙ The p value Is the mathematical probability that the relationship between variables found within the sample occurred by chance or sampling error ∙ In statistics, relationships are describe in a range from a p value of 0 to 1.00 (just as in probability) ∙ A p value of LESS THAN 0.05 is acceptable ∙ If a p value is GREATER THAN .05 there is more than a 5% chance that what we found is due to sampling error and we are not OK with that Statistical significance ∙ If there is less than a 0.05 (5%) chance that the results we obtained were obtained by chance, we say that the results are statistically significant ∙ P < .05 Research hypothesis ∙ Hypothesis we are trying to prove Null hypothesis ∙ If no support for the research hypothesis, then the null hypothesis was supported ∙ It’s a statement that no relationships exsist Research hypothesis: 2 types ∙ One tailed hypoethesis: is a directional hypothesis.this is where we predict the direction of the relationship between 2 variables. Ex. Group work is more effective in treating men who are abusive than individual work 15∙ Two tailed hypothesis: we believe there is a relationship, but we don’t know which direction, we would use a two tailed hypothesis or non-directional. Ex. There is a relationship between the type of treatment for men who are abuseive. Errors in drawing conclusions about relationships ∙ Type 1 error: in reality your hypothesis is wrong, but your research supports it ∙ Type 2 error: in reality your hypothesis is right, but the research supports the null 16