1 data analysis in quantitative and qualitative research

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Data Analysis in Quantitative and Qualitative Research

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Quantitative

Data

Analysis

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• Data collected in research studies needs to be systematically analyzed to determine trends and patterns of relationships.

• Statistical procedures are used to do this in quantitative research

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Levels of Measurement

• A system of classifying measurements according to the nature of the measurement and the type of mathematical operations (statistics) which can be used to measure it

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• Nominal measurement

• Ordinal measurement

• Interval measurement

• Ratio measurement

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• Nominal measurement– Uses numbers simply to categorize characteristics– Method of sorting data– Provides information only about categorical

equivalence and non-equivalence– Can not be treated mathematically (can’t be quantified)– Lowest level of measurement

• i.e. gender, blood type, nursing speciality• May assign males to be 1, females to be 2

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• Ordinal measurement– Ranks objects based on their relative standing on a

specific attribute– Rank orders– Limited ability for mathematical formula (quantifiable)

• i.e. lightest person to heaviest person• Tallest person to shortest• Totally independent to total dependent• Level of education – high school, BN, MN

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• Interval measurement– Ranking of objects on an attribute but also able to

specify the distance between those objects– Used for statistical procedures

• i.e. scholastic testing• Psychological testing

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• Ratio measurement– Ratio scales have a rational, meaningful zero– Provide information about the absolute magnitude of

the attribute– Used for statistical procedures– Highest level of measurement

• Blood pressure• Weight (200 pds is twice as heavy as 100 pds)• Intake / Output

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What is Statistics

• Statistical procedures enable the researcher to summarize, organize, interpret, and communicate numeric information

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Statistics

• Classification– Descriptive statistics– Inferential statistics

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Descriptive Statistics

• Are used to describe and synthesize data– i.e. averages and percentages

– Parameters• A characteristic of a population• Data calculated from a population

– i.e. mean age of all Canadian citizens

– Statistic• Data calculated from a sample• An estimate of a parameter

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• Most scientific questions are about parameters, researchers calculate statistics to estimate them

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• Methods researchers use to make sense out of descriptive data

– Frequency distributions– Central tendency– Variability

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• Frequency Distributions– Imposes order on numeric data– Systematic arrangement of numeric values from lowest to highest– Displays percentage of the number of times each value was

obtained

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• Frequency Distributions– Can be displayed in

• Frequency polygon– Graphically - scores on horizontal line, frequency (percentages) on vertical

line

0%20%40%60%80%

100%

1st Qtr 2nd Qtr 3rd Qtr 4th Qtr

North

West

East

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• Central Tendency– Seeks a single number that best represents the whole

distribution– Describes only one variable

• Mode• Median• Mean

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– Mode• The number that occurs most frequently in a distribution• The most popular value• Used for describing typical or high-frequency values for

nominal measures

• i.e. 5 10 6 10 9 8 10 (10)

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– Median (Md)• The point in the distribution where 50% of cases are above

and 50% of cases are below• The midpoint in the data• Insensitive to extreme values• Used with highly skewed distributions

• i.e. 2 2 3 3 4 5 6 7 8 9 (4.5)

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– Mean • Is equal to the sum of all values divided by the number of

participants• The average• Affected by the value of every score• Used in interval or ratio-level measurements• The mean is more stable than the median or mode

• i.e. 5 4 3 2 1 15/ 5 = (3)

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• Variability

– Variability is the spread of the data from the mean– The variability of two distributions could be different

even when the means are identical• i.e. could have a homogenous group with scores all clustered

together with the same mean as a heterogeneous group where scores are variable

– Need to know to what extent the scores in a distribution differ from one another

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• Variability– Used to measure the variability, the differences in

dispersion of data

• Range

• Standard Deviation

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• Range– Is the highest score minus the lowest score in a

distribution– Not a very stable method– Only based on two scores

» i.e. highest score 750, lowest score 250 range (500)

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– Standard Deviation (SD)• Calculated on every value in a distribution• Summarizes the average amount of deviation of values from

the mean• Most widely used measurement to determine variability of

scores in a distribution

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– Standard Deviation (SD)• The SD represents the average of deviations from the mean• Indicates the degree of error when a mean is used to

describe data

• In normal distributions there are three standard deviations above and below the mean

– i.e. 68% of cases fall within 1 SD above and below the mean– 95% of cases fall within 2 SD above and below the mean– 4% of cases fall more than 2 SD from the mean

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Standard Deviation Graph

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• Bivariate Descriptive Statistics– Bivariate (two variable)– Describes relationships between two variables

– Uses• Contingency Tables• Correlation

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– Contingency Tables• The frequency of two variables are cross-tabulated• Used for nominal or ordinal data

– i.e. look at both gender and non-smokers (two variables)

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– Correlation• Most common method of describing the relationship between

two variables• Calculate the correlation coefficient

– Describes the intensity and direction of the relationship– A formula that determines how perfect the relationship is– Positive relationship (+1.00), negative relationship (-1.00), no

relationship (0)– When two variables are positively correlated this means high values

on one variable are associated with high values on the other variable

– i.e. height and weight– Tall people tend to weight more than short people

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Inferential Statistics

• Entails formulas that provide a means for drawing conclusions about a population from the sample data

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• Sampling Distributions– When estimating population characteristics, you need

to obtain representative samples– Probability sampling is best– Inferential statistics should use only probability

sampling

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• Sampling error– As it is not possible to obtain a sample that is identical to the

population, a slight error is assumed– The challenge for researchers is to determine whether sample

values are good estimates of population parameters

• Standard error of the mean– The sample means of the distribution contain some error in their

estimates of the population– The smaller the standard error the more accurate are the means

as estimates of the population value

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• The more homogenous the population the more likely it is that the results from a sample will be accurate

• The larger the sample size, the greater is the likelihood of accuracy as extreme cases will cancel each other out

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• Uses two major techniques

– Estimation of Parameters– Hypothesis testing

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Estimation of Parameters

• Estimation procedures (estimation of parameters) are used to estimate a single population characteristic

• Not used often as researchers are more interested in relationships between variables

– i.e. oral temperature

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Hypothesis Testing

• Hypothesis– A prediction about relationships between variables

• Null Hypothesis– States that there is no relationship between the independent and

the dependent variables– Determining that the null hypothesis has a high probability of

being incorrect, lends support to the scientific hypothesis– Rejection of null hypothesis is accomplished through statistical

tests– Rarely stated in research reports

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Hypothesis Testing

• Provides objective criteria for deciding whether hypotheses should be accepted as true or rejected as false

• Assists researchers decide which results are likely to reflect chance differences and which are likely to reflect true hypothesized effects

• Researchers assume that the null hypothesis is true and then gather evidence to disprove it

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Hypothesis Testing

• Type l and Type ll Errors– Researchers decide whether to accept or reject the null

hypothesis by determining how probable it is that observed group differences are due to chance

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Hypothesis Testing

• Type l Error– Rejecting the null hypothesis when it is true

• i.e. concluded that the experimental treatment was effective when in fact the group differences were due to sampling error or chance

• Type ll Error– Accepting a false null hypothesis

• i.e. concluded that the observed differences were due to random sampling fluctuations when in fact the experimental treatment did have an effect

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Hypothesis Testing

• Level of Significance (alpha) is:

– The risk of making a Type l error, established by the researcher before statistical analysis

– The probability of rejecting the null hypothesis when it is true

– .05 level » accept risk that out of 100 samples, a true null hypothesis

would be rejected 5 times (5%)» Accept that in 95 of 100 cases (95%), a true null hypothesis

would be correctly accepted– .01 level

» Accept that 1 out of 100 samples, a true null hypothesis would be rejected (1%)

» Accept that in 99 of 100 cases, a true null hypothesis would be rejected (99%)

– .001 level » Accept that 1 out of 1000 samples, a true null hypothesis would

be rejected

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Hypothesis Testing

• Level of Significance (alpha)

– The minimal acceptable alpha level for scientific research is .05

– Lowering the risk for Type l error increases the risk of a Type ll error

– Can reduce the risk of Type ll error simply by increasing the sample size

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P Values (the probability value)

• Level of significance is sometimes reported as the actual computed probability that the null hypothesis is correct (based on research results)

– Can be reported as falling below or above the researcher’s significance criterion < or >

– P = .09 (9 out of 100 chance that observed differences between groups could be by chance)

– P < .05 (5 out of 100 chance that observed differences could be by chance)– P < .01 (1 out of 100 chance that observed differences could be by chance)– P < .001 (1 out of 1000 chance that observed differences could be by

chance)

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Hypothesis Testing

• Researchers reporting the results of hypothesis tests state that their findings are statistically significant

– Significance means that the results were most likely not due to chance

– The statistical findings supported the hypothesis

– Nonsignificant results means that the results may have been the result of chance

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What Does This All Mean?

• If a researcher reports that the results have statistical significance this means that based on statistical tests, the findings are probably valid and replicable with a new sample of participants

• The level of significance is how probable it is that the findings are reliable and were not due to chance

• If findings were significant at the .05 level this means that:– 5% of the time the obtained results could be incorrect or due to

chance– 95% of the time similar results would be obtained if you did

multiple tests, therefore the results were probably not due to chance

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Tips on Reading Statistical Information

• Information reported in the results section:

– Statistical information• Enables readers to evaluate the extent of any biases

– Descriptive statistics• Overview of participant's characteristics

– Inferential statistics • What test was used• Further statistical information

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Interpreting Study Results

• Must consider– The credibility and accuracy of the results– The meaning of the results– The importance of the results– The extent to which the results can be generalized– The implication for practice, theory, or research

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– The credibility and accuracy of the results• Accurate and believable• Based on analysis of evidence not personal opinions• External evidence comes primarily from the body of prior research• Research methods used• Note limitations

– The meaning of the results• Analyzing the statistical values and probability levels• It is always possible that relationships in the hypothesis were due to

chance• Non-significant findings represent a lack of evidence for either truth or

falsity of the hypothesis

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– The importance of the results• Should be of importance to nursing and the healthcare of the

population

– The generalizability of the results• The aim is to gain insights for improvement in nursing

practice across all groups and within all settings

– The implications of the results• How do the results affect future research• How do the results affect nursing practice

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• Analyzing Qualitative Data

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Qualitative Analysis

• Includes data from:• Loosely structured

narrative materials from interviews

• Field notes or personal diaries from personal observation

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• Purpose of Analysis– To organize, provide

structure, and elicit meaning from research data

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• Difficult to analysis data as:– Qualitative research does not have systematic rules for

analyzing data– A lot of work, very time consuming– Difficult to reduce data to report findings

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Qualitative Analysis: Styles

• Analysis Styles:– Quasi-statistical analysis style– Template analysis style– Editing analysis style– Immersion/crystallization analysis style

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Qualitative Analysis: Styles

– Quasi-statistical analysis style• Views narrative data for particular words or themes• Collects information that can be analyzed statistically

– Template analysis style• Uses a template to determine which narrative data are

analysed

– Editing analysis style • Codes and sorts data after the researcher has identified

meaningful segments

– Immersion/crystallization analysis style• Total immersion in and reflection on the materials

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Qualitative Analysis: Process

• Analysis Process:– Comprehending

• Completed when saturation has been attained

– Synthesizing• Putting the data together and making sense out of it

– Theorizing• Sorting the data and developing possible theories

– Recontextualizing• Developing theory further so it could be applied to other

settings or groups

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Qualitative Analysis: Procedures

• Organizing the Data:– Classify and index the material, identifying the concepts

– Reductionist – data is converted to smaller, more manageable units that can be retrieved and reviewed

– Develop categorization scheme, code data according to categories

– Constant comparison –collected data is compared continuously with data obtained earlier

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• Coding the Data:– Data are coded into appropriate categories

– Manual Methods• Develops files to sort concepts• Cuts out concepts from narratives for filing in concept folder

– Computer Programs• Indexes and retrieves data• Also can analyze data

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• Analyzing the Data– Constructionist – putting pieces together into a meaningful

pattern

– Begins with the search for relationships and themes in the data

– Validation that the themes are accurate representation of the phenomenon

• Investigator triangulation – using more than one person to interpret/analyze the data

• Member checks – share preliminary findings with informants to get their opinions

– Unites themes to develop theory

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• Grounded Theory Analysis– Generating theories and conceptual models from data

– Constant comparison – simultaneously collects, codes and analyzes data

– Uses coding – open and selective

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• Phenomenological Analysis– Describes the meaning of an experience, identifies

major themes

• Qualitative Content Analysis– The analysis of the content of narrative data to identify

prominent themes and patterns among the themes

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Interpreting Qualitative Results

• Credibility• Meaning• Importance• Transferability• Implications

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Reference

• Loiselle, C. G., Profetto-McGrath, J., Polit, D. F., & Beck, C. T. (2011). Canadian essentials of nursing research. (Third Edition). Philadelphia: Lippincott, Williams & Wilkins.

1 data analysis in quantitative and qualitative research

Documents

descriptive statisticsare

numeric information

quantitative research

levels of measurementa

quantitative data analysis

highfrequency values

frequency percentages

statistical proceduresi