research methodology for nursing students: data analysis

Department of Community Medicine and Public Health Universiti Malaysia Sarawak

Data Analysis

Dr Helmy Hazmi MD MComMed (Epid & Biostats)

[email protected]


The p value

The statistical significance.

P < 0.05 is significant.

P > 0.05 is not significant.

0.05


Newbie’s meaning of significant

A significant association between 2 variables.

A significant difference in mean between 2 variables.

A significant difference in mean before and after and intervention.

A significant correlation between 2 variables.

Chi square test.

Independent t test.

Paired t test.

Correlation test.


Hypothesis

An assumption.

A thesis

A prediction

For further investigation.

Use statistics to reject or accept hypothesis.

Null hypothesis

Alternative hypothesis


Null hypothesis, H0

States that:

There is no association between the variables of interest.

There is no difference in mean between the variables of interest.

Research examples:

There is no association between smoking and lung cancer.

There is no difference in mean BMI between the girls and boys in UNIMAS.


Alternative hypothesis, Ha

States that:

There is a significant association between variables of interest.

Thee is a significant difference in mean between the variables of interest.

Research examples:

There is a significant association between smoking and lung cancer.

There is a significant difference in mean BMI between boys and girls in UNIMAS.


What does significant really mean?

5% - amount of false alarms allowed. Relationship occurs at random / by chance.

95% - due to real association / difference. Not by chance.

Truth about the population

H0 TRUE(accept null hypothesis)

Ha TRUE (reject null hypothesis)

Decision based on sample (your study)

Accept Ho Correct decision Type 2 error, β

Reject HoType 1 error, α

(miss diagnosed/ false alarm/ false positive)

Power (1 – β)


The P - value

Based on α.

Based on the allowable type 1 error.

Critical value of α is 5% / 0.05

0.05 is the cut off point


If p value is 0.02

Percentage of type 1 error = 2%

False alarm = 2%

By chance (secara kebetulan) = 2%

Below critical limit, 5%

98% correct decision.

98% reflects true relationship.

Significant relationship.

Reject null hypothesis


If the p – value is 0.08

Percentage of type 1 error = 8%

False alarm = 8%

Relationship by chance = 8%

Above critical limit of 5%


92% true relationship.

Relationship not significant.

Accept null hypothesis.


Between smoking and lung ca, p=0.03

False alarm = 3%

Type 1 error made = 3%

By chance = 3%

Below 0.05.


97% real relationship.

Relationship is significant.

Reject null hypothesis.


Though there is an association between smoking and lung cancer, we do not know the direction yet.

Does smoking cause lung cancer? What is the odds of smokers to get lung cancer?

Further analysis needed.


Univariate statistical test

Relationship between an

INDEPENDENT

variable and a

DEPENDENT

variable.

Other possible concurrent factors omitted.

Smoking and lung cancer?

HPV infection and cervical cancer?

Knowledge and practice?

Sleep hours and exam score?


A guide to choosing a statistical test

Variable 1 Variable 2 Statistical test

Categorical Categorical Chi square test

Categorical (2 levels)

Numerical Independent t test

Numerical Numerical Correlation test

Pre intervention Post intervention Statistical test

Categorical Categorical Chi square test


Chi square test

Measure association

Between 2 categorical variables.

Traditionally, a 2 by 2 table.

Can go more, but risk small samples.

This is a 2 by 2table

Lung cancerYES

Lung cancer NO

Smoking YES A B

Smoking NO c D

This is a 3 by 2table

Lung cancerYES

Lung cancer NO

Ex smoker A B

Currently smoking

C D

Never smoke E F


Assumptions for chi square test

Categorical variables only.

Samples are random.

Mutually exclusive.

Cells with expected cell counts of <5 should not be more than 20% of total cells.


Go to

http://publichealthunimas.blogspot.com/

“download centre”

Download data .sav

http://publichealthunimas.blogspot.com/


Chi square steps

Analyse: Gender vs hypertension status

Analyse > Descriptive > Crosstab

Enter independent var in row | enter dependent var in column

Statistics > check [chi square] > continue

Cells > check [counts] [percentages] > continue

Ok


Output


The chi square value is read here

The p value is read here.

One of the assumption is to be checked here. If the % of expected cell counts of less than 5 is >20, perform fisher exact test and read the p value from fisher exact test row.


Interpretation

The p value is 0.521.

More than 0.05.

There is no significant association

between gender and hypertension

status


Independent t test

Categorical vs numerical variables.

Category must be 2 levels only.

Compare the mean between 2 levels.

Examples:

Compare mean BMI between males and females.

Compare blood glucose (mmol/l) between patients attending PK Mosque Rd and PK Tanah Puteh.

Compare mean age between high income and low income earners.


Assumptions of ind t test

Samples are random.

2 levels are mutually exclusive.

Normal distribution.

Dependent variables must be numerical

Homogeneity of variance.


Homogeneity of variance

Homogenous = same

Heterogenous = different

Variances are the same.

𝑠2 = 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛


Homogeneity of variance

S2 = 100

S2 = 200

Mean1 = mean2 BMI 23.0

Pop 2 has more people > BMI 23.0

Both populations are heterogenous.


Ind T Test steps

Analyse > compare means > ind samples t test

Insert numerical var in test variable

insert categorical var in grouping var

Define groups

Define groups for grouping var > continue > ok

Analyse: Gender vs age


Know your coding beforehand.


Output


The assumption of equality of variance is read here

The 95% Confidence interval is read here.The p-value is read here.


Interpretation

Mean age for male = 49.6

Mean age for females = 46.5

The p-value is 0.049

p-value is lower than 0.05

There is a significant

difference in mean age

between males and females.


Paired t test

Almost like independent t test.

Both groups are related

Not mutually exclusive.

Common examples:Mean BMI before and after exercise.


Assumptions of Paired t test

Samples are random

The two groups are related

Numerical dependent variable

Observed differences are normally distributed.


Related means

Not mutually exclusive

Occurrence affect the other.

“Before and after” test

Husband and wife


Notice how the data are entered


Steps

Analyse: BMI pre intervention vs BMI post intervention

Analyse > compare means > paired samples t test

Insert numerical var in test variable

insert categorical var in grouping var

Define groups

Define groups for grouping var > continue > ok


Check for assumption

Transform > compute variable

“BMI pre – BMI post”

Create the distribution curve.

Observe.


Analyse > Descriptive > Explore


The mean difference are normally distributed


Output


The p-value is read here.


Interpretation

The mean BMI before intervention

25.7

The mean BMI after intervention

23.8

P-value = 0.003

p-value less than 0.05

There is a significant

drop/difference of mean BMI

before and after the exercise intervention.


Correlation

Numerical vs numerical.

Strength of the relation

Direction of the correlation

Uses correlation coefficient

P value too.


Correlation coefficient magnitude

Positive correlation Negative correlation NO correlation


Strength of correlation

Pearson correlation

coefficient, r =

0.00 – 0.30: Negligible

0.031 – 0.50: Weak

0.51 – 0.80: Moderate

0.81 – 1.00: Strong

1.00: perfect correlation


r2 (extra information)

The r square.

Coefficient of determination.

Tells the fitness of data with the statistical model.

Square root it to get coefficient of correlation.


Relationship between r and p value

r = 0.9 r = 0.7 r = 0.3


Correlation assumption

Random samples

2 variables are normally distributed.

Mutually exclusive


Steps:

Analyse > correlate > bivariate

Enter variables of interest

OK

Analyse: correlation between weight and height


Read Pearson correlation coefficient, r, here

Read p- value here.


Interpretation

The Pearson correlation coefficient between weight and height 0.545.

The p-value is < 0.001

Less than 0.05

There is a significant correlation between

weight and height


For further understanding of your data


How to present in table

Descriptive

Chi square test

Independent t test

Paired t test

Correlation


Chi square


*** there should be “df” after chi square:

Chi square (df)


Independent t testAnd correlation


Paired t test


Correlation test

research methodology for nursing students: data analysis

Health & Medicine