STATS ex 2 - Selecting appropriate analysis techniques and elements of power analysis

Specific Related Factors research Suitability

1-4 identify statistical procedures that meet the requirements of a particular study

1- purpose of study

2- study hypotheses, question, objectives

3- study design

4- level of measurement of variables in a study

Specific Related Factors Research Suitability - 2

5-9 further narrow your options through process of elimination

5- previous experience in statistical analysis

6- statistical knowledge level

7- availability of statistical consultation

8- financial resources

9- access of knowledge of statistical software

specific related facts research suitability def

most important factor when choosing a statistical procedure is the study hypothesis or primary research question

• if it is clearly stated it will indicate the statistical test that is needed

purpose of this study is to determine if there is a difference in marital status (married/divorce) in couples who attended premarital counseling or not.

What type of statistic are we looking to use based upon this purpose statement?

Statistic to determine difference and it will be dichotomous (married/divorced - only 2 options)

purpose of this study is to determine if there is a difference in marital status (married/divorce) in couples who attended premarital counseling or not.

What is your dependent variable?

Marital status

purpose of this study is to determine if there is a difference in marital status (married/divorce) in couples who attended premarital counseling or not.

What is the independent variable?

Attended premarital counseling (yes/no)

nominal - dichotomous

purpose of this study is to determine if there is a difference in marital status (married/divorce) in couples who attended premarital counseling or not.

What type of variable is the dependent variable?

Nominal (dichotomous)

purpose of this study is to determine if there is a difference in marital status (married/divorce) in couples who attended premarital counseling or not.

What type of variable is the independent variable?

Nominal (dichotomous)

Decision Tree

• way of selecting appropriate statistical procedure or judging appropriateness of an analysis tech

• gradually narrows options based off decisions

• incorrect decision = led down wrong path

T-test for independent samples def

most common statistical tests to navigate the differences between two independent samples

T-test for ind. samples - options

parametric and inferential

only compares two groups at a time

dependent variable - continuous and normally distributed

• continuous - uncountable (infinite - age, distance, temp)

T-test for paired samples def.

also referred to as a dependent samples t-test

T-test for paired samples - options

compares two sets of data from one group of people

parametric and inferential

dependent variable must be continuous and normally distributed

repeated assessment of the same group of people

one way analysis of variance

ANOVA

One-way ANOVA def

statistical procedure that compares data between two or more groups or conditions to investigate the presence of differences between those groups

One-way ANOVA options

parametric and inferential

dependent variable - continuous & normally distributed

One-way ANOVA tests one ind variable and one dep variable

Repeated Measures ANOVA def

procedure that compares multiple sets of data from one group of people

Repeated Measures ANOVA options

dependent variable - continuous & normally distributed

indicated research design is to repeatedly assess same group of people over time

refer to naturally occurring pairs (siblings, spouses)

Mann-Whitney U

nonparametric alternative to independent samples t-test

Mann-Whitney U - about

compares differences between two independent samples

preferred when distribution of dependent variable data significantly deviates from normality or when dependent variable is ordinal and cannot be treated as interval/ratio scaled variable

Kruskal-Wallis Test

nonparametric alternative to the one-way ANOVA

Kruskal-Wallis - about

compares differences between two or more groups

preferred over ANOVA when the distribution of the dep variable data significantly deviates from normality or the dependent variable is ordinal and cannot be treated as an interval/ratio scaled variable

Friedman test

nonparametric alternative to the repeated measures ANOVA

Friedman test - about

compares multiple sets of data from one group of people

preferred over repeated measure ANOVA when the dep variable data significantly deviates from normality or the dep variable is ordinal and cannot. be treated as interval/ratio scaled variable

Wilcoxon Signed-Rank test

nonparametric alternative the the paired samples t-test

Wilcoxon Signed-Rank test - about

compares two sets of data from one group of people

preferred over the paired samples t-test the the dependent variable data significantly deviates from normality or if the dependent variable is ordinal and cannot be treated as an interval/ratio scaled variable

Pearson Chi-square test

nonparametric inferential statistical test that compares differences between groups on variables measured at the nominal level

Pearson Chi-square test - about

compared frequencies that are observed with those that are expected

can reveal if the differences in proportions (percentages) between categories is statistically improbable

One-way chi square

compared different levels of one variable

Two way chi square

tests whether proportions in levels of one nominal variable are significantly different than the proportions in a second nominal variable

Pearson product-moment correlation coefficient - ( r )

parametric, inferential statistic computed by two continuous, normally distributed variables

Pearson product-moment correlation coefficient - ( r ) - requirements

represented by statistic r

value of r is always between -1.00 and +1.00

value of 0 indicates no relationship

(+) correlation indicates that higher values of x are associated with higher values of y

(-) correlation indicates that lower values of x are associated with lower values of y

Spearman rank-order correlation coefficient

non parametric alternative to Pearson r

Spearman rank-order correlation coefficient - about

examines association between two continuous variables

preferred over the Pearson r when one or both variables significantly deviate from normality or the variables are ordinal and cannot be converted to interval/ratio

Phi

nonparametric alternative to Pearson’s r when the two variables being correlated and dichotomous

• phi yields a value between -1.0 and 1.0 and 0 represents no association

Cramer’s V

nonparametric alternative to the Pearson r when the two variables being correlated are both nominal

• Cramers V yields a value between 0 and 1 where a 0 represents no association between the variables and 1 represents a perfect association

Odds Ratio def

commonly used to obtain an indication of association when both the predictor (independent) and the dependent variables are dichotomous

Odds Ratio - about

defined as the ratio of the odds of an event occurring in one group to the odds of it occurring in another group

can be computed when the dependent variable is dichotomous and the predator is continuous and would be computed by performing a logistic regression analysis

Odds Ratio - necessities

• OR of 1.0 indicates that the predictor does not affect the odds of the outcome

• OR of >1.0 indicates that the predictor is associated with a higher odds of an outcome

• OR of <1.0 indicates that predictor data is associated with a lower odds of the outcome

Simple and Multiple Linear Regression def

procedure that provides an estimate of the value of the dependent variable based upon the value of an independent variable or set of independent variables (predictors)

Simple and Multiple Linear Regression - about

used to predict the value of one variable if we know the value of another

the score on variable y (dependent variable or outcome) is predicted from the same subjects known score on variable x (independent variable or predictor)

what statistic would be appropriate for an associational research question or hypothesis involving the correlation between two normally distributed continuous variables ?

Pearson Product Moment Corr. Coefficient ( r )

What statistic would be appropriate for a differences research questions involving the comparison of two repeated assessments from one group of participants, where the dependent variable is measured at the interval/ratio level or is continuous and the data are normally distributed?

Paired sample t-test

A statistics instructor wants to identify if there is a difference between face to face lecture and online lectures To do this she randomly assigned 150 students to each group of 42 hours of instruction each. She then offered an exam on the comprehensive level of knowledge of the students in both classes. The exa that was offered yielded a continuous score. What is the appropriate statistic to address the research question if the data was normally distributed ?

Independent samples t-test

A statistics instructor wants to identify if there is a difference between face to face lecture and online lectures To do this she randomly assigned 150 students to each group of 42 hours of instruction each. She then offered an exam on the comprehensive level of knowledge of the students in both classes. The exa that was offered yielded a continuous score. What is the appropriate statistic to address the research question if the data was not normally distributed ?

Mann-Whitney U

What statistic would be appropriate for a difference research question involving the comparison of three independent groups on a normally distributed continuous dependent variable?

One Way ANOVA

What statistic would be appropriate for an associational research questions involving the correlation between two non-normally distributed, skewed continuous variables?

Spearman Rank Order Correlation Coefficient

A statistics professor tests her students’ level of knowledge at the beginning of the semester and administers the same test at the end of the semester. She compares the two sets of continuous scores. Her research question is: Is there a difference in statistics knowledge from the beginning to the end of the semester? What is the appropriate statistic to address the research question if the data is normally distributed?

Dependent samples T-test

A statistics professor tests her students’ level of knowledge at the beginning of the semester and administers the same test at the end of the semester. She compares the two sets of continuous scores. Her research question is: Is there a difference in statistics knowledge from the beginning to the end of the semester? What is the appropriate statistic to address the research question if the data is not normally distributed?

Wilcoxon Signed Rank test

Power Analysis

can be conducted via hand calculations, computer software or online calculators and should be performed to determine and adequate sample size for the study

ex: G* Power, NCSS, CAC

Type I Error

occurs when the results of the study indicate that there is a significant difference between the groups when in actuality there is no difference

• incorrect rejection of a true null hypothesis

• a “false positive”

Type II Error

occurs when the results of the study indicate that there is not a significant difference when in fact there is

• incorrectly retaining a false null hypothesis

• a “false negative”

Power

deciding factor in determining an adequate sample size for descriptive, correlational, quasi-experimental tan and experimental studies

• the probability that a statistical test will detect an effect when it actually exists

• calculated as 1-B (complement of type II error)

Conventional value - power

0.20 (1-.20=0.800 = 80%

statistic will have 80 % chance of detecting an effect if an effect actually exists

more on Power

• can address the number of participants needed for a study

• power analysis should be performed before the study begins - this is called a priori power

• if performed after the study it is termed post hoc power analysis

Post-Hoc Power Analysis

should be reported in the results section of a study that fails to reject the null hypothesis

• if power was high ( i.e. .80) it strengthens the meaning of the findings (if a relationship was found)

Power Analysis KNOW THESE

knowing any of the three factors allowed the researcher to calculate the 4th

1) level of significance (a-level)

2) probability of obtaining a significant result (1-B) usually 0.80

3) hypothesized or actual effect (association or difference)

4) sample size

study slides for power analysis #1-6

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Effect size

indicates how strong the relationship is between variables and the strength of the differences between groups

the degree to which the phenomenon is present in the population or the degree to which null hypothesis is false

more on effect

essentially a prediction of the “effect” of the study

• target effect size would be selected if the researcher thought that the effect would be larger

• small effect sized require larger samples to detect the small differences

• However if the power is low only consider conducting the study if the sample is large enough to detect an effect (overall is the study worth it)