**Introduction**

**Question 1:**What are the required basic terms and concepts?

**Answer 1:**Inference is the act or process of deriving a logical consequence conclusion from premises.

*Figure 1. Using statistical analysis on sample(s) to make inferences about a population*

**1. Point estimation**, involving the use of sample data to calculate a single value (also known as a statistic), which is to serve as a “best guess” for an unknown (fixed or random) population parameter (e.g. relative risk RR = 3.72).

**2. Interval estimation**is the use of sample data to calculate an interval of possible (or probable) values of an unknown population parameter, in contrast to point estimation, which is a single number (e.g. confidence interval 95% CI for RR is 1.57-7.92).

*Figure 2. The concept of true value, point estimation and confidence interval***3. Prediction/forecast**- forecasting is the process of estimation in unknown situations. A prediction is a statement or claim that a particular event will occur in the future in more certain terms than a forecast, so prediction is a similar, but more general term. Risk and uncertainty are central to forecasting and prediction.

**4. Statistical hypothesis testing**- last but not least, probably the most common way to do statistical inference is to use a statistical hypothesis testing. This is a method of making statistical decisions using experimental data and these decisions are almost always made using so-called “null-hypothesis” tests.

_{0}) formally describes some aspect of the statistical behavior of a set of data and this description is treated as valid unless the actual behavior of the data contradicts this assumption.

_{1}). Statistical tests actually test the null hypothesis only. The null hypothesis test takes the form of: “

*There is no difference among the groups*” for difference tests and “

*There is no association*” for correlation tests. One can never “prove” the alternative hypothesis. One can only either reject the null hypothesis (in which case we accept the alternative hypothesis), or accept the null hypothesis.

**Question 2:**Why do we need statistical inference and its principal exponent – statistical hypothesis testing?

**Answer 2:**In a few words, because we need to demonstrate in a scientific manner that, for example, an observed difference between the means of a parameter measured during an experiment involving two samples, is “statistically significant” (4).

*Table 1. The results from the experiment***Question 3:**What steps are required to apply a statistical test?

**Answer 3:**

_{0}) if S > CV and vice versa. Practically, if P ≤ α, we will reject the null hypothesis; otherwise we will accept it (4).

**Choosing the right statistical test. What do we need to know before we start the statistical analysis?**

**Question 4:**What type(s) of data may we obtain during an experiment?

**Answer 4:**Basic data collected from an experiment could be either quantitative (numerical) data or qualitative (categorical) data, both of them having some subtypes (4).

**The quantitative**(numerical) data could be:

**1. Discrete (discontinuous)**numerical data, if there are only a finite number of values possible or if there is a space on the number line between each 2 possible values (e.g. records from an obsolete mercury based thermometer).

**2. Continuous data**, that makes up the rest of numerical data, which could not be considered discrete. This is a type of data that is usually associated with some sort of advanced measurement using state of the art scientific instruments.

**1. Interval data**- interval data do not have an absolute zero and therefore it makes no sense to say that one level represents twice as much as that level if divided by two. For example, although temperature measured on the Celsius scale has equal intervals between degrees, it has no absolute zero. The zero on the Celsius scale represents the freezing point of water, not the total absence of temperature. It makes no sense to say that a temperature of 10 on the Celsius scale is twice as hot as 5.

**2. Ratio data**- ratio data do have an absolute zero. For example, when measuring length, zero means no length, and 10 meters is twice as long as 5 meters.

**The qualitative**(categorical) data could be:

**1. Binary (logical) data**- a basic type of categorical data (e.g. positive/negative; present/absent etc).

**2. Nominal data**- on more complex categorical data, the first (and weakest) level of data is called nominal data. Nominal level data is made up of values that are distinguished by name only. There is no standard ordering scheme to this data (e.g. Romanian, Hungarian, Croatian groups of people etc.).

**3. Ordinal (ranked) data**- the second level of categorical data is called ordinal data. Ordinal data are similar to nominal data, in that the data are distinguished by name, but different than nominal level data because there is an ordering scheme (e.g. small, medium and high level smokers).

**Question 5:**How could be these data types organized, before starting a statistical analysis?

**Answer 5:**Raw data is a term for data collected on source which has not been subjected to processing or any other manipulation (primary data) (4).

**1. Indexed data**– when we will have at least two columns: a column will contain the numbers recorded during the experiment and another column will contain the “grouping variable”. In this manner, using only two columns of a table we may record data for a large number of samples. Such approach is used in well known and powerful statistical software, such as SPSS (developed by SPSS Inc., now a division of IBM) and even in free software like Epiinfo (developed by Center for Disease Control - http://www.cdc.gov/epiinfo/downloads.htm) or OpenStat (developed by Bill Miller,http://statpages.org/miller/openstat/).

**2. Raw data**– when data are organized using a specific column (row) for every sample we may have. Even if this approach may be considered more intuitive from the beginner’s viewpoint, it is used by a relative small number of statistical software (e.g. MS Excel Statistics Add-in, OpenOffice Statistics or the very intuitive Graphpad Instat and Prism, developed by Graphpad Software Inc.).

**Question 6:**How many samples may we have?

**Answer 6:**Depending on the research/study design, we may have three situations (4,7):

*post hoc*tests are available, used if the null hypothesis is rejected at the second stage of the analysis of variance and able to make comparison between each and every pair of samples from the experiment.

**Question 7:**Do we have dependent or independent samples/paired or unpaired groups?

**Answer 7:**In general terms, whenever a subject in one group (sample) is related to a subject in the other group (sample), the samples are defined as “paired”.

**Question 8:**Are the data sampled from a normal/Gaussian distribution(s)?

**Answer 8:**Based on the normality of distributions, we chose parametric or nonparametric tests.

*a priori*assume that we have sampled data from populations that follow a Gaussian (normal/bell-shaped) distribution. Tests that follow this assumption, are called parametric tests and the branch of statistical science that uses such tests is called parametric statistics (4).

**Question 9:**When may we choose a proper nonparametric test?

**Answer 9:**We should definitely choose a nonparametric test in situations like these (7):

**1. D’Agostino-Pearson normality test**– which computes the skewness and kurtosis to quantify how far from normality the distribution is in terms of asymmetry and shape. It then calculates how far each of these values differs from the value expected with a normal distribution, and computes a single P-value from the sum of these discrepancies. It is a versatile and powerful (compared to some others) normality test, and is recommended by some modern statistical books.

**2. Kolmogorov-Smirnov test**– used often in the past - compares the cumulative distribution of the data with the expected cumulative normal distribution, and bases its p-value simply on the largest discrepancy, which is not a very sensitive way to assess normality, thus becoming obsolete.

**3.**Beside of these two, there are a relatively large number of other normality tests, such as: Jarque

**-Bera test, Anderson-Darling test, Cramér-von-Mises criterion, Lilliefors test for normality**(itself an adaptation of the Kolmogorov-Smirnov test),

**Shapiro-Wilk test, the Shapiro–Francia test for normality**etc.

*Table 2. Parametric versus nonparametric tests***Question 10:**Shall we choose one-tailed or two-tailed tests?

**Answer 10:**Let’s imagine that we design some studies/experiments to compare the height of young male adults (18-35 years) between various countries in the world (e.g between Sweden and South Korea and another, between Romania and Bulgaria). So, during a statistical analysis, a null hypothesis H

_{0}(e.g. there is not a difference between the heights mean for those two independent samples) and an alternative hypothesis H

_{1}for the specific statistical test has been formulated. Let’s consider that the distribution is Gaussian and the goal is to perform a specific test to determine whether or not the null hypothesis should be rejected in favor of the alternative hypothesis (in this case t-test for unpaired/independent samples will be the relevant one).

*Figure 3. Critical regions in one-tailed and two-tailed tests***Question 11:**What is the goal of our statistical analysis?

**Answer 11:**When using basic statistical analysis, we may have, at most, three main goals (4,7):

*Table 3. Statistical tests that compare the means (medians) for one, two, three or more groups/samples*

*Figure 4. The selection process for the right statistical test*