# research variables-selecting statistics

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25/03/55

Khon Kaen University

Khon Kaen University

(Research variables)

A variable is something that can change any observation that can take different values (Southard,2006) a condition or quality that can differ from one case to another

Khon Kaen University

Khon Kaen University

Theoretical framework Pre-specified research agenda Curiosity-driven research** 1. 2. 1. 2. 3.

1. (independent v.) (dependent v.) (quantitative or continuous v.) (qualitative or discreet v.) Dummy variables

2.

1.1. 2.

Continuous vs. Discrete Variables

(independent variable) (control) (explanatory) (predictor) plot X

(quantitative or continuous v.) (qualitative or discreet or categorical v.) / 2 Khon Kaen University

3.

2.1. 2. 3.

(dependent v.) outcome, response, or explained variable plot Y

Khon Kaen University

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Khon Kaen University

Khon Kaen University

alcohol 50 10-100 alcohol 2 alcohol ( ) alcohol

1. ... 2. ()

1. 2. /

Levels (scales) of measurement Nominal scales Ordinal (rank) scales Interval scales Ratio scales(Foster, 2001; Miller & Salkind, 2002)

Khon Kaen University

Khon Kaen University

1. Nominal Level (/) ( / ) /

2. Ordinal or Ranking Level

/ ( )

Khon Kaen University

Khon Kaen University

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3. Interval Level ordinal level + IQKhon Kaen University

4. Ratio Level Interval level + true zero points

() Khon Kaen University

Deciding the nature of variable> 2 categories Variable is dichotomous No Yes Distances b/w categories equal? No Variable is ordinal Yes Can categories Be rank ordered?

Variable is Interval / ratio

Yes

Variable is Nominal

NoKhon Kaen University

Types of Data Quantitative data Ordinal Interval Ratio ok to use statistical procedures

T = 35-37.5 C = normalT = 37.5-38.4 = mild fever

Categorical & Frequency Many stats cannot be used meaningfully

Khon Kaen University

Khon Kaen University

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Khon Kaen University

Qualitative Analysis (informants)

Donwiwat Saensom Faculty of Nursing, KKU

/

Khon Kaen University

Qualitative Analysis (transcription) grounded theory, phenomenological analysis, content analysis / (trends & patterns)

Khon Kaen University

Quantitative Data Analysis spreadsheet database (trends & patterns) (descriptive statistics) median, mode

Khon Kaen University

Khon Kaen University

Quantitative Analysis trends & patterns (correlation, causalrelationships etc)

2 Descriptive vs Inferential Statistics 1. : continuous vs discrete 2. types of measurement scale 3. statistical analysis 4. Within subjects Between-subjects 5. Directional vs Non-directional 6. significance test (Foster, 2001)Khon Kaen University

Interpretation & Explanation final report

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Descriptive vs. Inferential Statistics Descriptive statistics XX 6

Parametric vs. Non-parametric

Inferential statistics test hypotheses sample population i.e. Khon Kaen University

Parametric stats : interval or ratio scales Non-parametric stats: ordinal scale, and assumptions parametric stats Nominal scales use non-parametric e.g. chi-squareKhon Kaen University

Khon Kaen University

Khon Kaen University

Parametric Assumptions1. 2. 3.

interval or ratio levels (normal distribution)Kolmogorov-Smirnov test

(variance) homogenous (Homogeneity of variance) 4. (Independence of5.

Levene test

scores) Random sampling from defined populationBryman & Cramer, 2001

Khon Kaen University

Khon Kaen University

Nonparametric statistics

Parametric statistics

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Within subjects vs. Between-subjects Related/ within-subject comparisons 2 Independent/ between-subject comparisons Khon Kaen University

Directional vs. Non-directional Hypotheses Directional (one-tailed) hypotheses (-) ( ) Khon Kaen University

Choosing Statistics Depending on

Choosing the correct statistical tests 1. 2. 3. samples/groups 4. 5. Khon Kaen University Khon Kaen University

Research questions Nature of data

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Research questions Generally 2 purposes Exploring differences between/among scores on variables Exploring relationships between/among variables

Statistical tests corresponding to research questions (Bryman & Cramer, 2001)1. Bivariate analysis1.1 Exploring differences 1.2 Exploring relationships

2. Multivariate analysis2.1 Exploring differences 2.2 Exploring relationshipsKhon Kaen University

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Exploring Differences (Bryman & Cramer, 2001) Categorical data non-parametric test Ordinal & interval/ratio data either is possible Related or unrelated comparison groups? Compare means or variances? Mostly compare differences between means Differences between variances is used when the variances differ markedly (thus means differences are not reliable)

Tests of differences(Bryman & Cramer, 2001)Nature of Criterion Variables Type of test Type of data Number of comparis on groups 1 1 2+ 2 3+ Name of test

Categorical NonUnrelated Nominal or parametric Related frequency

Two or more comparison groups?Khon Kaen University

Binomial Chi-square Chi-square McNemar Cochran Q

Tests of differences(Bryman & Cramer, 2001)Nature of Criterion Variables Type of test Type of data Number of comparison groups Name of test

Exploring Relationships (Bryman & Cramer, 2001)Level of Measurement Nominal-nominal Nominal-ordinal Ordinal-ordinal Interval-interval Measure of Association Contingency-table analysis + Chi-square Cramers V can be used to test for strength of association Spearmans rho or Kendalls tau Pearson r for strength of relationship Regression for character of relationship Contingency-table analysis + Chi-square Phi can be used to test for strength of association Rho or tau when the ordinal variable has a large number of categories Contingency-table analysis is use dwhen there are few categories in both ordinal and interval variables Contingency-table analysis + Chi-square if the interval variable can be sensibly collapsed into categoriesKhon Kaen University

Noncategorical

Nonparametric

Unrelated

1-2 2 2+ 3+ 2 3+

Kolmogorov-Smirnov Mann-Whitney U Median Kruskal-Wallis H Sign, Wilcoxon Friedman

Related

Dichotomous-dichotomous

Parametric: means

Unrelated Related Related and unrelated

1-2 2+ 2 2+ 2+ 2+

t-test One-way and 2-way ANOVA Paired t-test Single factor repeated measure 2-way ANOVA with repeated measure on one factor Two-way analysis of covariance

Interval-ordinal

Interval-nominal Interval-dichotomous

Khon Kaen University

Common measures of association Pearson product correlation (r ) .. (interval) Correlation ratio (eta) . (interval) Spearmans rank differences coefficient, rho . (ordinal) Lambda . (Nominal) Multiple regression, R (interval)

Khon Kaen University

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Khon Kaen University

Khon Kaen University

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