Student’s of variance ANOVA. In this study, we mainly

Student’s T Test compares the significant difference
between two groups (two means). In this study, paired t-test is used to compare
groups and test the significant difference between two sets of data. If the
data are significant given by the P ??0.05 were considered as significant data,
P < 0.01*, P < 0.001**, P < 0.0001***. The multiple t-test compares the statistical significance probabilities analysis for several t-tests at once. The two-way ANOVA used to compare independent variables of interest and to understand if there is an interaction between them in different conditions. Our hypothesis findings needed more common hypothesis tests such as two-way analysis of variance ANOVA. In this study, we mainly have two independent factors that are autophagy and IR with different time points. This basic research begins with a question that whether autophagy inhibition is more effective for the PCa patients' treatment combined with radiotherapy (RT) rather than RT treatment alone. To test this question, we need to transform basic question to a testable hypothesis, labeled H0 named as a Null hypothesis, which takes the following form: H0: Whether autophagy inhibition is NOT more effective for the PCa patients' treatment combined with RT rather than RT treatment alone. To test this hypothesis, we harvested the samples from PCa cell lines as explained in (2.2 Cell culture and treatments) and measured the results in order to decide whether the data from that experiment provides a strong evidence in order to reject the H0 or not. If our evidence is strong to reject H0, then we are indirectly accepting the alternative hypothesis (Ha), which is: autophagy inhibition is more effective for the PCa patients' treatment combined with RT rather than RT treatment alone. For each experiment, we collected the samples data to define our hypothesis involving its finding by using the decision rule whether reject the null hypothesis or not. The null hypothesis is rejected if the p-value is less than a predetermined level, ?. ? is called the significance level, and is the probability of rejecting the null hypothesis given that it is true (a type I error). It is usually set at or below 5%. and the p-value is a number between 0 and 1 and interpreted in the following way: A small p-value (typically ? 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.

The probability of an outcome can be rejected when the p-value is ??0.05. In
student’s (paired) t-test, computed data of the difference between two samples
before and after IR treatment were as followed: calculating the mean by
counting foci numbers/ nuclei, that included >30 foci/field. Each experiment
was repeated 3 times as indicated by (n=3), to allow calculation of the average
mean of the gathered data. For example, H0: autophagy has no role on
the DNA-damage response (DDR) signaling in response to ionizing radiation (IR)
treatment. In contrast, Ha: autophagy regulates the DDR signaling in response
to IR treatment; we examined it in autophagy-deficient PCa cells.

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Immunostaining showed that the number of ?H2AX IR-induced foci (IRIFs) at 0.5h
were not significantly different between dox-pretreated cells followed by IR
compared to IR treatment alone in LNCaP (Fig 3.2. a and b). To explain it
statistically, the probability of forming ?H2AX foci is 0.0955, which is larger
than 0.05, that leads to decreased evidence against H0. However,
autophagy-deficient cells revealed persistent ?H2AX foci at 24h following IR
treatment compared to the parental cells following IR alone. The probability of
which is <0.0001, this is much less than 0.05, hence the evidence against H0 is strong and it can be rejected. Under the assumption that the null hypothesis is true, we repeated large number of random samples (>30 foci/field) to test
H0 and Ha. The significance level (a)=
0.05, which indicates 5% of the difference exists in the distribution. We can
also see if it is statistically significant using the other common significance
level of 0.01. This time our sample mean does not fall within the critical
region and we fail to reject the null hypothesis.

This probability represents the likelihood of obtaining a
sample mean that is at least as extreme as our sample mean in both tails of the
distribution depending on the average mean. Hence, significance levels and P
values are important tools that help us quantify and control this type of error
in a hypothesis test. Using these tools to decide when to reject the null
hypothesis increases our chance of making the correct decision.            All assumptions should include
appropriate positive and negative controls. It is also valuable to distinguish
between assessments that have a reproducible quantitative readout on how data
will be tested across treatment groups for significance, and rules for data
exclusion. Indeed, it is difficult to predict a scenario where this would not
benefit scientific rigor, replicability and reduce bias. One possible that
needs to confirm biological replicates by using different samples are
independent from another lab.