Chapter 15-Inferential Statistics

Level of Significance

represented by alpha how willing is the researcher to be wrong. --probability of rejecting the null hypothesis when it is true. (most common level .05-5%-5/10) may be as specific as .001 such as when deciding if a drug is effective

Multivariate analysis of variance (MANOVA)

-examines difference between mean scores of two or more groups on two or more independent variables that are examined at the same time

Mean square within (MSW)

-groups examine variation of individual scores within each of the groups

Mean square between (MSB)

-groups explore variation between the means of groups

Effect size

-indicates how useful a treatment or intervention was in several studies indicated by the difference between data from control and experimental groups -reported as small, medium or large

Non-parametric Tests

-less stringent requirements and do not make assumptions about population from which sample is selected -called distribution free statistics -used with nominal and ordinal data -sample sized may be small

Chi squared

-non parametric -used to compare sets of nominal data -observed frequencies compared to expected frequencies -null is rejected if the observed frequencies are quite different from the expected frequencies at a specific level of significance -used to determine if observed values might have occurred by chance

T Test

-parametric test that examines the difference between mean values of some variable in two groups -used for small samples (fewer than 30) -interval or ratio is required

Analysis of covariance (ANCOVA)

-powerful stat test used when researcher wishes to control statistically for some variable that may have an influence on dependent variable ie= determine if anxiety levels of open heart surgery will be lower if the group receives a pictorial info about post op procedures rather than verbal

critical value

-scientific cutoff point -denotes the value in a theoretical distribution at which all obtained values are equal to or beyond the point of distribution -Found in tails -determined by level of significance and degree of freedom

Meta-analysis

-technique that combines the results from several quantitative studies that have been conducted on the same topic

Meta-synthesis

-technique used in summarizing reports of qualitative research studies, combines results of several studies that cover the same topic

Null Hypothesis

subjected to statistical analysis, it states no difference exists between variables and population. Inferential stats are based on the assumption that no difference exists. 1)If small difference or low correlations are found=not rejected 2.If large difference or correlation is found=rejected (not based on chance)

Critique of research reports

reader should 1.Search the report for any inferential statistics that were used in data analysis -determine if there is enough info to make a decision on appropriateness of each test -Be provided with the value of the statistical test that was obtained, the degree of freedom, and significance level that was reached when each hypothesis was tested -be able to determine if each of the researcher's hypothesis was supported or not -every report should clearly present results of hypothesis testing in both text and tables

Canonical correlation

-examines correlation between two or more independent and dependent variables

Confidence intervals

(CI) range of values with a specific degree of probability is thought to contain the population value. --Includes lower limit (LL) and upper limit (UL)

Advanced Statistical Tests

-Multiple regression -Analysis of co-variance (ANCOVA) -Canonical correlation -multivariate analysis of variance -Meta-analysis -Meta-synthesis

rules of ANOVA

-Null hypothesis true, MSB, MSW very similar and less than one -Null hypothesis is false, MSB, MSW greater than one and bigger difference between groups -Difference between groups greater than difference within= null is rejected -difference between is not significantly greater than within= null hypothesis is rejected

Power of statistical test

-ability to reject null hypothesis when it is false -more powerful the test, more likely to detect significant difference or correlation -dependent on sample size and level of significance chosen -larger sample size the more power the test -high level of significance the more power the test -one-tailed test is more powerful -if assumptions of parametric tests are met, more powerful than non parametric tests

Parametric Tests

-concerned with population parameters, these tests make assumptions about the population from which the sample was drawn -interval or ratio -data taken from populations that are normally distributed on the variable being measured -data taken from populations have EQUAL variance on the variable being measured

Degree of freedom

-df -number of the values that free to vary -concern is more focused on number of values not free to vary ie- pick a number 1-10 (df-10) ie-pick number three numbers that add to ten, you pick 3 and 5, the third number is not free to vary because it must be 2.

Analysis of variance (ANOVA)

-used to compare differences in more than two groups (ie:effectiveness of four different methods in teaching clients how to give insulin injections) -difference between several means at one time -parametric test (based on assumption) -F distribution based on DF

Two-tailed test

-used when non directional hypothesis is used -used to determine significant values on both ends of the sampling distribution. -harder to reject null hypothesis

One-tailed test

-used when researcher states direction of hypothesis -differences or correlations are sought in only one tail of the theoretical sampling (right or left tail) -easier to reject null hypothesis

Multiple regression

-used when researcher wishes to determine the influence of more than one independent variable on the dependent variable ie=determine what factors would most accurately predict a women's decision to perform SBE

Dependent t test

-used when scores or values are associated or have some connection (ie: anxiety scores of mothers and daughters if matched on some variable such as age or weight) -also obtained when the same subjects are measured before and after receiving some type of experimental treatment -paired t test, correlated t test

Critical region or region of rejection

-where critical value lies

Questions for choosing stat test

1. Are you comparing groups or sets of scores? Are you correlating variables 2.What is the level of measurement of variables? 3.How large are the groups? 4.How many groups or sets are being compared? 5.Are the observations or scores dependent or independent? 6.How many observations are available for each group?

Choosing a Stat test

1. Concerned with significant difference between groups (ie:experimental and control) 2 Is there a significant correlation between variables within one group (ie:levels of pain reported and number of requests for pain medication)

Forms of t tests

1. Independent 2. Dependent

Steps in Testing Hypothesis

1. state 2.Chose appropriate stat test 3.Decide level of significance 4.Decide one or two tailed test 5.Calculate the test stat 6.Compare calculated value to critical value 7.reject or fail to reject null hypothesis 8. determine support or lack of for hypothesis

Purposes of Inferential Statistics

1.Estimate population parameters from the sample 2.Test hypothesis

Inferential Statistics

all based on the assumption that chance (sampling error, or random error) is the only explanation for the relationships that are found in the research study -The larger the difference between the groups, the lower the probability that the difference occurred by chance -The larger the correlation between variables the greater the likelihood that the variables are in fact correlated in the population

Standard error of the mean

indicates that when sampling distribution of the mean is used to represent a population some error is likely to occur. --The smaller that standard error of the mean the more confident the reflection of the population of the mean--

tail

indicated values of each end of a distribution

Independent t test

no association or connection between scores of the groups being observed (ie: experiment and control group being compared) -independent samples t test or unrelated samples t test

Type II error

null hypothesis is actually false and you fail to reject it -determined by power analysis

Type I error

null hypothesis is actually true but you reject it -determined by level of significance

Computed value is less then critical value

null hypothesis is not rejected

Computed value is greater than or equal to critical value

null hypothesis is rejected

Sample error

occurs when the sample does not accurately reflect a population

Central limit theorem

phenomenon in which samples tend to be normally distributed around the population (Ie pulse rate average 71, most have values close not many have values that are very different than the population)

Sampling distribution

theoretical frequency distribution based on an infinite number of samples. Distribution is theoretical because you never have an infinite number of samples in a population. Decisions are based on ONE sample. based on "what ifs" not actual data

Clinical significance

used in clinical setting however, statistically significance and clinical significance do not go hand in hand. Findings that are clinically significant do not always have to be statistically significant and vise versa.