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Foundations of Nursing Research, Sixth Edition
Rose Marie Nieswiadomy
Note slide 12
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FOUNDATIONS OFNURSING RESEARCH
Sixth Edition
CHAPTER
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Inferential Statistics
15
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Learning Objective One
Recall The Two Purposes Of Inferential
Statistics
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Broad Purposes of Inferential
Statistics
• Estimating population parameters from
sample data (after data collection)
Parameter = symbols
• Testing hypotheses (before data
collection)
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Learning Objective Two
Discuss The Sampling Distribution Of The
Mean
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Sampling Distribution of the Mean
• Approximates the normal curve
• Larger samples are more adequate
• :القانون تاعها
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Standard Error of the Mean
• Standard deviation of the sampling
distribution of the mean
• Symbolized ˆ
– Smaller ˆ value means it is more likely the
sample is an accurate reflection of the
population mean.
.كل ما كانت نسبتها عالية كل ما كانت الثقة اقل
x
x
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Learning Objective Three
Define Terms Used In Inferential Statistics
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Inferential Statistics
• Central limit theorem
– Tendency of sample values to be normally
distributed around population value
• Sampling distribution
– Theoretical frequency distribution based on
infinite samples
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Confidence Interval
• CI
• Range thought to contain the population value
• Includes lower and upper limit, with specified degree of
probability
يعني لو اخذت عينة واخذتلهم الافريج فراح اشوف قديش راح يكون من لو اخذت
الافريج لمجتمع الدراسة كاملا
: القانون مع مثاللين موجودين بالصفحات القادمة
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X pare= mean of sample
1.96= هي عدد ثابت لكنه بختلف حسب النسبة يلي اختارها الباحث
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شايفين هون انه الثابت تغير لانه النسبة يلي اختارها الباحثتغيرت
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Hypotheses
• Directional research hypothesis
– Predicts results of study
• Null hypothesis
– No difference exists between populations or
no correlation exists between variables in the
population.
– (H0)
– Subjected to statistical analysis
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Hypotheses (cont’d)
• Null
– Rejected or retained
• Research
– Supported or not supported
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Level of Significance
• Probability level of rejecting a null
hypothesis when it is true
• Symbolized by letter p and Greek letter
alpha (α)
• The most common probability level in
nursing research is p = .05.
• If result <p = reject H 0
• If result >p = fail to reject H 0
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Inferential Statistics
• Critical value
– Value in a theoretical distribution at which all
obtained sample values that are equal to or
beyond that point in the distribution are said to
be statistically significant
• Critical region or region of rejection—all
values beyond the critical value
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Degrees of Freedom
• Symbolized (df)
• Concerns the number of values that are free to vary
• Interpretation of statistical tests dependent on the
degrees of freedom
• ف 10الى 1لو طلبنا تختارولنا رقم من : 1مثال
Degree of freedom =10
ف 10ارقام يكون مجموعهم 3لو طلبنا انه تختاروا : 2مثال
DF= 2
لانه بس اول رقمين بقدر اتحكم فيهم
*increase freedom = increase possibility
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Learning Objective Four
Distinguish Between A One-tailed And A
Two-Tailed Test
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One-Tailed Versus
Two-Tailed Tests
• One-tailed tests
– Appropriate for directional research
hypotheses
– Degree of difference or type of correlation
predicted
– Easier to reject the null hypothesis
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One-Tailed Versus
Two-Tailed Tests
• Two-tailed tests
– Appropriate for nondirectional research
hypotheses
– Difference or correlation predicted, but the
degree is not indicated
– More difficult to reject the null hypothesis
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Learning Objective Five
Describe Type I And Type II Errors
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Errors
• Type I error
– Null hypothesis is actually true, but is rejected.
مماثل للالفا
• Type II error
– Null hypothesis is actually false and it is retained.
مماثل للبيتا
Power analysis الها علاقة مع
Acceptance when H0 is false
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• Power analysis = 1-B
Ex : 100/100 – 20/100 = 80/100
لازم يكون في موازنة بين نوعي الخطا لانه زيادة تحكم بواحد
منهم بيزيد احتمالية حدوث الاخر لكن الباحثين عادة بهتموا
بانه يضبطوا النوع الاول اكثر من النوع الثاني واي واحد اخطر بيتحدد حسب الموقف
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Learning Objective Six
Differentiate Between Parametric And
Nonparametric Statistical Tests
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Parametric Tests
• Population parameters
Very powerful
Act to assumption of population
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Parametric Tests
• Make assumptions about the population from which a
sample was drawn
– The level of measurement of the data is interval or
ratio.
– Data taken from populations that are normally
distributed on the variable that is being measured
– Data taken from populations that have equal
variances on the variable that is being measured
If violation occur to any assumption , use nonparametric
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Nonparametric Tests
• Distribution-free statistics (more flexible )
– Makes no assumptions about the distribution
of the population
• May be used with nominal and ordinal
data
• Sample sizes may be small.
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Learning Objective Seven
Discuss The Power Of A Statistical Test
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Power of a Statistical Test
• Ability of the test to reject a null hypothesis
when it is false
• Dependent on the sample size and the
level of significance that is chosen
• The larger the sample size chosen, the
more power the statistical test has.
• The higher the level of significance
selected, the more power the statistical
test has.
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Power of a Statistical Test (cont’d)
• A one-tailed test is more powerful than a
two-tailed test.
• If the assumptions of parametric tests are
met they are more powerful than
nonparametric tests.
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Learning Objective Eight
List Criteria For Selecting A Statistical Test
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The T Test
• Parametric test assumptions
• Compares the difference between mean
values of some variable in two groups
• Particularly useful for small sample sizes
• Interval or ratio data required
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Analysis of Variance (ANOVA)
• Parametric statistical test
• Compares differences among more than
two means at one time
• Based on assumptions that data
– Are interval or ratio level
– Have been selected from populations that are
normally distributed
– Have equal variances on the variable that is
being measured
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• Different between and in groups
• F=MSB(between group ) / MSW(within group )
Result :
F<1 = H0 true
MSB>MSW = rejection of H 0
F >1 = H0 false
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Chi-Square (χ2)
• Nonparametric inferential technique
• Used for comparing nominal sets of data
• Used to inform any group is more
significant different between the groups
when using ANOVA
• Result put in contingency table
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ex
•In this example the variable is :
1-type of nurses
2- smoking status
• 50فبيطلع المربع الواحد 4بقسمهم على 200المجموع بقارن بيلي بتوقعه مع يلي تم مشاهدته •
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Learning Objective Nine
Identify Statistical Tests Commonly
Reported In Nursing Studies
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t Tests
• Parametric test that examines differences
between the means of two groups of
values
• Independent t test or unrelated samples t
test
– Test for samples with no association or
connection
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t Tests (cont’d)
• Dependent t test or paired t test
– Used when scores or values are associated
or have some connection
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Analysis of Variance (ANOVA)
• Examines the two types of variances in
data obtained
– “Mean square between” (MSB) groups
explore variation between the means of the
groups.
– “Mean square within” (MSW) groups examine
variation of individual scores within each of
the groups.
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Chi-Square (χ2)
• Observed frequencies are compared to
expected frequencies.
• Null hypothesis is rejected if the observed
frequencies are quite different from the
expected frequencies at a specified level
of significance.
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Advanced Statistical Tests
• Multiple regression
تحليل الانحدار / التنبؤ
Use to inform affect of independent of dependent variable
بدي اشوف ايش العوامل يلي بتزيد من حدوث الجلطة الدماغية : مثال
• Analysis of covariance (ANCOVA)
Statistical control
Freezing to one variable
No one affect other (dependent or outcome )
• Canonical correlation
• Multivariate analysis of variance (MANOVA)
اكثر من جروبين او اكثر من متغيرين بوقت واحد
• Meta-analysis
• Metasynthesis
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Learning Objective Ten
Critique The Inferential Statistics Section
Of Research Reports
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Critique of Research Reports
• Minimal understanding of inferential
statistics is sufficient.
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Critique of Research Reports
(cont’d)
• Reader should
– Search the report for any inferential statistics
that were used in data analysis
– Determine if there is enough information to
make a decision about the appropriateness of
each test that was used
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Critique of Research Reports
(cont’d)
• Reader should
– Be provided with the value of the statistical
test that was obtained, the degrees of
freedom, and the significance level that was
reached when each hypothesis was tested
– Be able to determine if each of the
researcher’s hypotheses was supported or
not
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Critique of Research Reports
(cont’d)
• Every research report should clearly
present the results of hypothesis testing in
both the text of the report and in the
tables.