- To determine if your data is statistically significantly different from the specified mean from T-test results
- To understand the basic descriptive statistics about your data
- To understand the descriptive statistics plot such as box-plot, mean-sd plot, QQ-plot, distribution histogram, and density distribution plot about your data to determine if your data is close to a normal distribution

- Your data contain only 1 group of values (or a numeric vector)
- The values are independent observations and approximately normally distributed

- The band inside the box is the median
- The box measures the difference between 75th and 25th percentiles
- Outliers will be in red, if existing

- Normal Q–Q Plot: to compare randomly generated, independent standard normal data on the vertical axis to a standard normal population on the horizontal axis. The linearity of the points suggests that the data are normally distributed.
- Histogram: to roughly assess the probability distribution of a given variable by depicting the frequencies of observations occurring in certain ranges of values
- Density Plot: to estimate the probability density function of the data

**Normal Q–Q plot**

**Histogram**

When the number of bins is 0, plot will use the default number of bins

**Density plot**

- P Value < 0.05, then the population of the data IS significantly different from the specified mean. (Accept the alternative hypothesis)
- P Value >= 0.05, then the population of the data IS NOT significantly different from the specified mean. (Accept the null hypothesis)

*Because P < 0.05, we concluded that the age of the lymph node-positive population was significantly different from 50 years old. Thus the general age was not 50. If we reset the specified mean to 44, we could get P > 0.05*

- To determine if the means of two sets of your data are significantly different from each other from T test results
- To know the basic descriptive statistics about your data
- To know the descriptive statistics plot such as box-plot, mean-sd plot, QQ-plot, distribution histogram, and density distribution plot about your data to determine if your data is close to normal distribution

- Your data contain 2 separate groups/sets (or 2 numeric vectors)
- The 2 separate groups/sets are independent and identically approximately normally distributed

- The band inside the box is the median
- The box measures the difference between 75th and 25th percentiles
- Outliers will be in red, if existing

- Normal Q–Q Plot: to compare randomly generated, independent standard normal data on the vertical axis to a standard normal population on the horizontal axis. The linearity of the points suggests that the data are normally distributed.
- Histogram: to roughly assess the probability distribution of a given variable by depicting the frequencies of observations occurring in certain ranges of values
- Density Plot: to estimate the probability density function of the data

**Normal Q-Q plot**

**Histogram**

When the number of bins is 0, plot will use the default number of bins

**Density plot**

- P value < 0.05, then refer to the
**Welch Two-Sample t-test** - P Value >= 0.05, then refer to
**Two-Sample t-test**

*In this example, P value of F test was about 0.15 (>0.05), indicating the equal variance in the data. Thus, we should refer to the results from 'Two-Sample t-test'*

- P Value < 0.05, then the population means of the Group 1 IS significantly different from Group 2. (Accept the alternative hypothesis)
- P Value >= 0.05, then there are NO significant differences between Group 1 and Group 2. (Accept the null hypothesis)

*In this example, we concluded that the age of lymph node positive population with ER positive was not significantly different from ER negative (P=0.55, from 'Two-Sample t-test')*

- To determine if the difference of the paired 2 samples are equal to 0
- To know the basic descriptive statistics about your data
- To know the descriptive statistics plot such as box-plot, mean-sd plot, QQ-plot, distribution histogram, and density distribution plot about your data to determine if your data is close to normal distribution

- Your data contain 2 separate groups/sets (or 2 numeric vectors)
- Two samples that have been matched or paired
- The differences of paired samples are approximately normally distributed

- One person's pre-test and post-test scores
- When there are two samples that have been matched or paired

- The band inside the box is the median
- The box measures the difference between 75th and 25th percentiles
- Outliers will be in red, if existing

- Normal Q–Q Plot: to compare randomly generated, independent standard normal data on the vertical axis to a standard normal population on the horizontal axis. The linearity of the points suggests that the data are normally distributed.
- Histogram: to roughly assess the probability distribution of a given variable by depicting the frequencies of observations occurring in certain ranges of values
- Density Plot: to estimate the probability density function of the difference

**Normal Q-Q plot**

**Histogram**

When the number of bins is 0, plot will use the default number of bins

**Density plot**

- P Value < 0.05, then Group 1 (Before) and Group 2 (After) have a significantly unequal effect. (Accept the alternative hypothesis)
- P Value >= 0.05, then there is NO significant difference between 2 groups. (Accept the null hypothesis)

*From the default settings, we concluded that the drug has no significant effect on the sleep hour. (P=0.2)*