UNIT V: Analysis of Non-numerical and Numerical Data SWK 330 Kimberly Baker-Abrams In qualitative research: analysis is on going (occurs as data is gathered) must be careful not to draw conclusions before all data is gathered Qualitative data analysis is less standardized than quantitative analysis because: researchers rarely know specifics at beginning analysis does not draw on established body of knowledge narrative is more imprecise than numbers Grounded Theory inductive process of discovering theory from data theory is created from and grounded in observations and measurements The basis of qualitative analysis is often a description - this includes: all collected information in-depth overview of all aspects of study s constraints The analysis process occurs by: assembling data organizing, classifying, and editing chronological or thematic narrative categories and codes for content use of code-book use of indigenous categories
Folk Terms versus Cover Terms Folk - terms or categories used by the subjects Cover - terms or categories used by the researcher Domain Analysis is: process of putting data into categories looking for: similarities and differences, flow of data, themes and theory that connect the data often involves a visual display of data (see text p. 226) In qualitative analysis the emphasis is on finding patterns, understanding events and using models to present what is found. The alternative hypothesis is: a test hypothesis (to be ruled out) the qualitative equivalent for null hypothesis Triangulation is important because: the more connected the ideas are to multiple sources the more likely you have validity Looking for missing information is as important in qualitative research as is connecting existing data. The missing information is often referred to as Negative Evidence.
Forms of negative evidence include: events that do not occur a population not being aware of events a population wanting to hide certain events a population overlooking common events effects of preconceived notions unconscious and conscious non-reporting Addition issues to consider for non-numerical data analysis: What points of view are not included? What do the events look like from the perspective of broader society? Has care been given to be sensitive to vulnerable populations and other social divisions? Results of analysis should: be understandable and meaningful to the population that was studied (and broader society as well). Descriptive statistics: a means of summarizing the characteristics of a sample or the relationship among variables Considerations for a frequency distribution: accurately describing the number of times a value occurs in a sample incomplete data is important to consider use of visual representation (text ch. 12) Extremely satisfied Satisfied Neutral Dissatisfied Extremely dissatisfied TOTAL N 12 19 7 B 4 50 Chuck + Tony Brad+Herb+Karen Rosina+Peter+Leon Kathy+Vincent+ Raquel + Mar o Rashad + Antoinette Shant + Rosemar e + Clarisse lvlarquerite + Elwin David Total... "/" 'r4% 380k 14Yo T6% 8% 100% Absolute Age Frequency 21 2 oj 273 31 4 322 373 492 69 1 20 Cumulative 7o Z4o/o 620k 760k s2% l OOo/o
TABLE 10.11 Observed and Expected Frequenc es: Type of Treatment and Gender of Client by Cl ent Outcome (N = 100) Cl ent Outcome Success Failures Treatment Gender Observed Expected Observed Expected Totals Group Male 7 (10) 18 (15) 25 Group Female I (10) 17 (15) 25 lndividual fvale 13 (1 o) 12 (15) 25 lndividual Female 12 (10) 13 (15) 25 lota s 40 60 loo y'1 = 4.334, d{ = 3, p>.05 (direction predìcted) EXAMPLE OF FREOUENCY POLYGON Frequency 50 45 40 35 30 25 20 '10 5 8 10 12 14 16 18 20 22 24 26 28 30 32 34 etc' lndividual lncome (in Thousands of Dollars) Measures of central tendency Mode (most common) Median (middle point) Mean (average - most commonly used) If the values form a normal distribution it will present as a bell-shaped curve. In a normal distribution, the three measures of central tendency are equal.
If the values are not equal the result is a skewed distribution ( a distribution in which most of the scores are concentrated at one end of the distribution rather than in the middle text). Number of Cases Normal Distribution Mode Median Mean "should we score the opposìhon by ønnouncing our meon height or lull them by onnouncing our medion height?" The measures of central tendency summarize the characteristics of the middle of the distribution, other characteristics of a distribution include the spread, dispersion and deviation. These characteristics are referred to as the measures of variability or measures of dispersion. Range the distance between the highest and lowest values used at interval and ratio level to calculate subtract the lowest value from the highest value = range
Standard deviation Percentile a number that divides the range of a data set so that a given percentage lies below this number most comprehensive and widely used measure of variation used at ratio or interval levels a measure of variability that averages the distance of each value from the mean only calculated by hand when there are few cases (see text 245-247) / I tlsot" 130/" I 13.59% -2SD - 1SD Mode I I Mediãn I I Meen I f--*,*o l_s5.44% 34.13% 34.130/. \t 13.5s% \ I 2.r5% 13%-.- + 2SD.+ 3SD FIGURE 4.8 Proponions of the Normal Curve Analysis that involves two or more variables is called bivariate or multivariate. Cross-tabulation (contingency table) examination of the dependent variable using the independent variable useful at any measurement level distribution of cases into categories to show which are contingent upon other variables
Correlation plotted on a chart called a scattergram correlation is shown by how closely the values approximate a straight line (+ - or curved) In using descriptive statistics (whether univariate or multivariate) the most effective way to describe them is to display the results visually. Interpreting graphs Level (change = discontinuity) Stability Trends (pattern within phase = slope, pattern across phases = drift)
I I 1 Reducing Trantrums Baseline (A) lntervention (B) o ø12 ; 10 / bf 'r b4.o Êc 5_ z 12 3r4 5 6 t 12 ø lu 3= B co Fo 6 Ê, oe bg 4 -o z 12 \ t.. discontinuity stability In graphing data X axis = independent variable (horizontal) Y axis = dependent variable (vertical) Trends Y dependent X
Types of graphs 100 lzo 140 160 Bar graph Histogram FrequencY Stem & Leaf 159 c624 ã o 56688e t 7 1144,ä i sstttttt77788e99 e I 0144++ 38558 195 1 10 3 Stem and Leaf Plot B.S.W 120 100 c o 980 (l) o ts60 õ) _o -^ E4u 5 z 20 s 6 g 12 15 18 21 24 27 Annual income (in thousands of dollars) Frequency Curve (line graph) FIGURE 2.3 DÌstribution of Social Workers at XYZ Agency by Degree (N = 100) Pie Chart
Scatterplot Graphs and statistics can be deceiving. Be aware of any graph that does not have an absolute zero point for Y or that has a discontinuous scale. 160 Graph A 150 140 1 1 11 100 90 80 70 60 r975 1976 1977 1973 1979 1930 1931 1932 1933 1934 1935 1036 19S7 1933 1939 1990 1991 1992 400 Graph B 350 300 250 200 T 150 100 \ 50 0 r97s 1S76 1977 1973 1979 r93o 1931 lo32 19 3 1934 1935 1936 1937 1933 1939 1990 1991 1992
Going beyond simply describing the data with descriptive statistics, you will use inferential statistics to test a hypothesis. Inferential statistics: precise method for deciding confidence in results from a sample method for deciding if a relationship between variable exists relies on probability theory There are two forms of hypothesis Two-tailed (non-directional): states there is an association between variables but gives no prediction about type of relationship One-tailed (directional): states that there is an association between variables and gives a prediction for type of relationship From the hypothesis, a null hypothesis is created. The null hypothesis: the test hypothesis asserts that any relationship between variables is due to chance A finding is considered to be statistically significant when the null hypothesis can be rejected and the probability that the result is due to chance falls at or below the study s given significance level.
The power of a statistical test is its ability to reject the null hypothesis. The power to reject the null hypothesis increases with the sample size. Errors in judgment concerning the acceptance or rejection of the null hypothesis are referred to as Type I and Type II errors. Type I error rejection of null hypothesis false conclusion that a relationship exists when in fact it does not Type II error acceptance of null hypothesis failure to recognize that a relationship does in fact exist between variables When a research study has a normal distribution and the dependent variable is measured at least at the interval level and the independent variable has been measured at the nominal level - the differences between the groups of data can be found using a T-Test. A T-Test a bivariate statistical test used to determine whether two groups are significantly different based on a particular characteristic
degrees of freedom (df) the number of values in the final calculation of a statistic that are free to vary you know that value of the mean, therefore it is not free to vary, to calculate df take the total number of cases (-) one (n-1) T-test involve two means, therefore to calculate a df take the total number of cases (-) two (n-2) In social work, it is common for research to involve three or more samples of data to compare. This is when an analysis of variance is used (ANOVA). ANOVA used to test differences between the means of three or more groups (one-way anova) Another way to analyze bivariate data is to examine the strength of the relationships between variables using correlation coefficients. Pearson s r: correlation coefficient used to asses the strength of a relationship ranges from -1 to +1 The regression line in a scatterplot graph is used to show how much change has occurred in the dependent variable are due to changes in the independent variable (prediction of change).
"How díd I get into fhis business? Well, I c< uldn't understond multiple regressíon snd correlshon in cctllege, so I settled lor this insteød." Multiple regression analysis produces a coefficient that allows each particular outcome (interaction between variables) to be evaluated in direction and the amount of change. Chi-Square analysis (X 2 ): one of the most widely used statistical tests in social work research. As a descriptive statistic: strength of association between variables As an inferential statistic: probability that association between variables is due to chance To use chi-square: you must first know what to expect from data (did results differ from expected) if a difference exists, there may be an association between variables X 2 = 0 then independence X 2 = more, then there is an association There are three types of significance in analysis of group data and single-subject studies. 1. Practical or clinical significance 2. Visual significance 3. Statistical significance
auto-correlation the relationship between the outcome or dependent variable scores in single-system studies (the sample is not statistically independent) A method to lessen the chance of auto-correlation is using a celeration line: connecting the midpoints of two values of the baseline and projecting the line into the intervention period if a given proportion of data are on the desired side of the celeration line, then an estimate of significance can be made In looking at the same results on a curve distribution, if the intervention mean is more than two standard deviations from the baseline mean, then there is a statistically significant change. In using inferential statistics, make sure to choose the most appropriate test for your data... and be sure to present the findings in as neutral a manner as possible.