# DHYG 440. Statical test. Mathematics & Economics Assignment. (Essay Sample)

DHYG 440

Research Methodology

Week 7

Statistical Significance

Used to determine the probability that the null hypothesis is true

There is no rule that dictates at what probability level the null hypothesis should be rejected

However, it is suggested that <0.05 or less is reasonable because they are low probabilities (such as .01 or .001)

An alternative way for a researcher to state they have rejected the null hypothesis is to state the difference is statistically significant

Statistical significance refers to the likelihood that the intervention had an effect for example, the results did not occur by chance at a specified probability level and the differences would still exist each time the experiment was repeated

Reported as the probability related to chance or “p ” level

Used to determine the probability that the null hypothesis is true

Ex. If a researcher conducted a significance test and found the probability that the null hypothesis is less than 5 in 100, this would be stated at p<.05 (p=probability)

Null hypothesis would be rejected

P-value

p<0.05 reject the null hypothesis (statistically significant)

p.>0.05 accept the null hypothesis (no statistical significance)

Clinical Significance

Clinical significance is used to distinguish the importance and meaning of the results reported in a study and is not based on a comparison of numbers, as is statistical significance.

It is possible for a study to have statistical significance without being clinically significant and vice versa

Measure of Central Tendency

Measure of Central Tendency: is a term used when describing the mean, median, and mode

Each of these measures calculates the location of the central point using a different method

This is a summary statistic that represents the center point or typical value of a dataset

Mean

Average

Balance point in a distribution; positive and negative deviations balance each other out, causing deviations to balance out to zero

Add up the scores and divide by the number of scores

x=mean

Ex. 7+8+9+10=34/4=8.5 x=8.5

Median

Middle Score

Describes the averages of skewed distributions

Put the scores in order from low to high, then count to the middle Ex. 9, 4, 2, 8, 7, 10, 6, 3, 5

2,3,4,5,6,7,8,9,10

Median=6

Mode

Most frequently occurring score

Very seldom reported in formal reports of research

Ex. 7,9,9,7,7,7,6,5,7

Mode=7

Standard Deviation

Describes variability; standardized method for describing the variability of normal distributions

Variability: amount by which participants vary or differ from each other

A set of scores is often described with two statistics, mean and standard deviation

This is a number used to tell how measurements for a group are spread out from the average (mean), or expected value

A low standard deviation indicates that values tend to be close to the mean of the set

A high standard deviation indicates the values are spread out over a wider range

Ex. 0,5,10,15,20,25,30

Mean=17.5, Standard Deviation=5

Chi-Square

Testing a null hypothesis for differences between frequencies (ex. Number of cases or n)

Used for nominal variables

Substep in the mathematical procedure for obtaining the value of p

When the probability (p) is 0.05 or less, the difference is statistically significant (reject the null hypothesis)

Symbol is x 2

t-Test

Often used to test the null hypothesis regarding the observed difference between two means

Symbol is t

ANOVA

Analysis of Variance

Two means are compared in a t-test, whereas ANOVA can compare a number of means

Indicates whether a set of differences is significant overall

One-way ANOVA: participants have been classified in only one way (ex. Classified by which drug was taken)

Two-way ANOVA: participants have been classified in 2 ways (ex. Which drug was taken and how long participants have been depressed)

Shapes of Distributions

One way to describe quantitative data is to prepare a frequency distribution

It is easier to see the shape of a distribution when the data is displayed in a figure

This gives a visual summary of the data and helps the researchers to see the distribution of data

Normal curve: smooth bell-shaped curve; variables are normally distributed

Skewed: have a tail on one side and not the other Positive skew: tail is to the right

Negative skew: tail is to the left

*See figures on p.213-214

Normal Curve

Skewed Curves

Frequency

Measure of how often an event occurs on average during a unit of time

Researchers may refer to frequency as numbers of cases or number of individuals, whose symbol is N

Can be reported as percentages

Example:

Females 52.2% (n=282) Males 47.8%(n=258)

Total 100% (N=540)

Some researchers report proportions instead of percentages

Ex. 258/540=0.48

obtain percentage by multiplying by 100=48%

Reporting of Research Results

Quantitative Research: researchers do not indicate how the statistical results were computed

For example the statistical tests that were used may be reported in the Methods section; the researcher would report which descriptive statistics that were used first (mean, standard deviation, and percentage), followed by the results of statistical significance Ex. Descriptive statistics: sd=1.50, m=24.00; Statistical tests: chi square, t-test,

ANOVA

Reporting of Research Results

Qualitative Research: there is usually a discussion of the steps taken to analyze the data

The method of analysis should be named and the steps taken to implement the method described

Few statistics are reported in the results section

Qualitative researchers discuss the primary themes that emerged from the data, as well as any theories developed during the analysis (narrative terms)

Screening Test

Objective of a screening test is to categorize individuals who are asymptomatic as being at high or low risk of a particular disease or condition, and not to make a definitive diagnosis. Further diagnostic procedures are then required for those who screen positive in order to

determine their true status

Diagnostic Test

Objective of a diagnostic test is to establish an actual diagnosis and is often based on the presence of signs and/or symptoms of a condition or disease.

*Screening and diagnostic tests need to have a high degree of accuracy in identifying the presence or absence of a disease

Sensitivity: is the proportion of people with disease or condition who have a positive test Conversely a test with low sensitivity will fail to detect disease/condition in many of those who actually have it, yielding a false-negative result

The test should have high sensitivity to be accurateSpecificity: is the proportion of people free of a disease who have a negative test

Conversely a test with low specificity will falsely indicate disease in many of those who do not have it, thus yielding in a false-positive result

The test should have high specificity to be accurate

Type I Error

When a researcher rejects a null hypothesis at exactly the 0.05 level, there are 5 chances in 100 that the null hypothesis is correct

The possibility that a null hypothesis is rejected when it is, in fact, a correct hypothesis, this is called a Type I Error

Rejecting the null hypothesis when it is actually true

AKA “False Positive”

Type II Error

When researchers fail to reject the null hypothesis, they are also taking a chance of making an incorrect decision

Perhaps the null hypothesis should have been rejected, but the significance test failed to lead the researchers to the correct decision, this is called a Type II Error Failing to reject the null hypothesis when it is actually an incorrect hypothesis; research

hypothesis is right and null hypothesis is not AKA “False Negative

Prompt:

Write 1 paragraph (4-5 sentences) on 2 statistical tests that you learned about this term. Also, describe what the p-value means in regards to accepting and rejecting the null hypothesis.

Statistical Test

Your Name

Subject and Section

Professor’s Name

January 4, 2021

Among the kinds of statistical tests that I have learned through the semester were; (1) the Chi-Square and (2) the ANOVA. On the one hand, the Chi-square (represented as x2) is primarily used for testing the significance of nominal variables.

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